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Can't solve system of linear equations (that need simplification first)

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5

1

$begingroup$

I'm self-studying from Stroud & Booth's amazing "Engineering Mathematics", and am stuck on a problem at the end of the "Linear Equations" chapter.

I've a system of two linear equations:

$$frac3x+24 - fracx+2y2 = fracx-312$$
$$frac2y+15 + fracx-3y4 = frac3x+110$$

So, these two first need to be simplified. I assume that the LSM for the first one (for 2, 4 and 12) is 12, so we have:

$$12frac3x+24 - 12fracx+2y2 = 12fracx-312$$

Simplifying further, we have:

$$3(3x+2) - 6(x+2y) = (x-3)$$
$$9x + 6 - 6x - 12 y = x - 3$$
$$9x -6x -x - 12y = -3 +6$$

Finally, we get our first simplified linear equation:
$$2x - 12y = 3$$

Now, onto the second one. The LSM of 5, 4 and 10 is 20, so we have:

$$20frac2y+15 + 20fracx-3y4 = 20frac3x+110$$

Simplifying further, we have:

$$4(2y+1) + 5(x-3y) = 2(3x + 1)$$
$$8y + 4 + 5x - 15y = 6x + 2$$
$$5x - 6x + 8y - 15y = 2 - 4$$

We get our second simplified linear equation:
$$-x -7y = 2$$

Now we can solve our system of linear equations:
$$2x - 12y = 3$$
$$-x -7y = 4$$

Multiplying the second one by 2:
$$2x - 12y = 3$$
$$-2x -14y = 4$$

Now, we add the two equations, and get:
$$-26y = 7$$

Solving for $y$, we get:
$$y = -frac726$$

which I'm fairly certain is not a correct answer.

Can anyone see where I'm going wrong here?

algebra-precalculus self-learning

share|cite|improve this question

edited Apr 23 at 17:03

neuron

asked Apr 23 at 11:57

neuronneuron

29217

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  When you take the $+6$ from the left hand side to the right hand side of the equal sign in the first equation you must switch its sign and it wil become $-6$. And in the second equation $2-4=-2$ and not $2$. So you'll get that $y=frac12$ at the end
  $endgroup$
  – Fareed AF
  Apr 23 at 12:04
  
  

  
  
  
  

add a comment | 

5

1

$begingroup$

I'm self-studying from Stroud & Booth's amazing "Engineering Mathematics", and am stuck on a problem at the end of the "Linear Equations" chapter.

I've a system of two linear equations:

$$frac3x+24 - fracx+2y2 = fracx-312$$
$$frac2y+15 + fracx-3y4 = frac3x+110$$

So, these two first need to be simplified. I assume that the LSM for the first one (for 2, 4 and 12) is 12, so we have:

$$12frac3x+24 - 12fracx+2y2 = 12fracx-312$$

Simplifying further, we have:

$$3(3x+2) - 6(x+2y) = (x-3)$$
$$9x + 6 - 6x - 12 y = x - 3$$
$$9x -6x -x - 12y = -3 +6$$

Finally, we get our first simplified linear equation:
$$2x - 12y = 3$$

Now, onto the second one. The LSM of 5, 4 and 10 is 20, so we have:

$$20frac2y+15 + 20fracx-3y4 = 20frac3x+110$$

Simplifying further, we have:

$$4(2y+1) + 5(x-3y) = 2(3x + 1)$$
$$8y + 4 + 5x - 15y = 6x + 2$$
$$5x - 6x + 8y - 15y = 2 - 4$$

We get our second simplified linear equation:
$$-x -7y = 2$$

Now we can solve our system of linear equations:
$$2x - 12y = 3$$
$$-x -7y = 4$$

Multiplying the second one by 2:
$$2x - 12y = 3$$
$$-2x -14y = 4$$

Now, we add the two equations, and get:
$$-26y = 7$$

Solving for $y$, we get:
$$y = -frac726$$

which I'm fairly certain is not a correct answer.

Can anyone see where I'm going wrong here?

algebra-precalculus self-learning

share|cite|improve this question

edited Apr 23 at 17:03

neuron

asked Apr 23 at 11:57

neuronneuron

29217

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  When you take the $+6$ from the left hand side to the right hand side of the equal sign in the first equation you must switch its sign and it wil become $-6$. And in the second equation $2-4=-2$ and not $2$. So you'll get that $y=frac12$ at the end
  $endgroup$
  – Fareed AF
  Apr 23 at 12:04
  
  

  
  
  
  

add a comment | 

$begingroup$

I'm self-studying from Stroud & Booth's amazing "Engineering Mathematics", and am stuck on a problem at the end of the "Linear Equations" chapter.

I've a system of two linear equations:

$$frac3x+24 - fracx+2y2 = fracx-312$$
$$frac2y+15 + fracx-3y4 = frac3x+110$$

So, these two first need to be simplified. I assume that the LSM for the first one (for 2, 4 and 12) is 12, so we have:

$$12frac3x+24 - 12fracx+2y2 = 12fracx-312$$

Simplifying further, we have:

$$3(3x+2) - 6(x+2y) = (x-3)$$
$$9x + 6 - 6x - 12 y = x - 3$$
$$9x -6x -x - 12y = -3 +6$$

Finally, we get our first simplified linear equation:
$$2x - 12y = 3$$

Now, onto the second one. The LSM of 5, 4 and 10 is 20, so we have:

$$20frac2y+15 + 20fracx-3y4 = 20frac3x+110$$

Simplifying further, we have:

$$4(2y+1) + 5(x-3y) = 2(3x + 1)$$
$$8y + 4 + 5x - 15y = 6x + 2$$
$$5x - 6x + 8y - 15y = 2 - 4$$

We get our second simplified linear equation:
$$-x -7y = 2$$

Now we can solve our system of linear equations:
$$2x - 12y = 3$$
$$-x -7y = 4$$

Multiplying the second one by 2:
$$2x - 12y = 3$$
$$-2x -14y = 4$$

Now, we add the two equations, and get:
$$-26y = 7$$

Solving for $y$, we get:
$$y = -frac726$$

which I'm fairly certain is not a correct answer.

Can anyone see where I'm going wrong here?

algebra-precalculus self-learning

share|cite|improve this question

edited Apr 23 at 17:03

neuron

asked Apr 23 at 11:57

neuronneuron

29217

$endgroup$

share|cite|improve this question

edited Apr 23 at 17:03

neuron

asked Apr 23 at 11:57

neuronneuron

29217

share|cite|improve this question

edited Apr 23 at 17:03

neuron

asked Apr 23 at 11:57

neuronneuron

29217

asked Apr 23 at 11:57

neuronneuron

29217

asked Apr 23 at 11:57

neuronneuron

29217

3 Answers
3

active

oldest

votes

8

$begingroup$

The first mistake I see is here:

$$9x + 6 - 6x - 12 y = x - 3$$ $$9x -6x -x - 12y = -3 +6$$

The second line should read

$$9x-6x-x-12y=-3-6$$

you forgot to invert the sign when moving $6$ to the other side of the $=$ sign.

---

You were equally sloppy with the second equation, when you did this:

$$5x - 6x + 8y - 15y = 2 - 4$$

We get our second simplified linear equation: $$-x -7y = 2$$

In fact, $2-4$ is not equal to $2$.

share|cite|improve this answer

answered Apr 23 at 12:06

5xum5xum

93.2k395162

$endgroup$

add a comment | 

2

$begingroup$

The first equation simplifies to $$2x-12y=-9$$ and the second one to $$-7y-x=-2$$

share|cite|improve this answer

answered Apr 23 at 12:01

Dr. Sonnhard GraubnerDr. Sonnhard Graubner

79.6k42867

$endgroup$

add a comment | 

1

$begingroup$

Finally, we get our first simplified linear equation:
This step is wrong:

$2x-12y=-9$ this should be your first equation.

share|cite|improve this answer

answered Apr 23 at 12:02

HS SinghHS Singh

112

$endgroup$

add a comment | 

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8

$begingroup$

The first mistake I see is here:

$$9x + 6 - 6x - 12 y = x - 3$$ $$9x -6x -x - 12y = -3 +6$$

The second line should read

$$9x-6x-x-12y=-3-6$$

you forgot to invert the sign when moving $6$ to the other side of the $=$ sign.

---

You were equally sloppy with the second equation, when you did this:

$$5x - 6x + 8y - 15y = 2 - 4$$

We get our second simplified linear equation: $$-x -7y = 2$$

In fact, $2-4$ is not equal to $2$.

share|cite|improve this answer

answered Apr 23 at 12:06

5xum5xum

93.2k395162

$endgroup$

add a comment | 

8

$begingroup$

The first mistake I see is here:

$$9x + 6 - 6x - 12 y = x - 3$$ $$9x -6x -x - 12y = -3 +6$$

The second line should read

$$9x-6x-x-12y=-3-6$$

you forgot to invert the sign when moving $6$ to the other side of the $=$ sign.

---

You were equally sloppy with the second equation, when you did this:

$$5x - 6x + 8y - 15y = 2 - 4$$

We get our second simplified linear equation: $$-x -7y = 2$$

In fact, $2-4$ is not equal to $2$.

share|cite|improve this answer

answered Apr 23 at 12:06

5xum5xum

93.2k395162

$endgroup$

add a comment | 

$begingroup$

The first mistake I see is here:

$$9x + 6 - 6x - 12 y = x - 3$$ $$9x -6x -x - 12y = -3 +6$$

The second line should read

$$9x-6x-x-12y=-3-6$$

you forgot to invert the sign when moving $6$ to the other side of the $=$ sign.

---

You were equally sloppy with the second equation, when you did this:

$$5x - 6x + 8y - 15y = 2 - 4$$

We get our second simplified linear equation: $$-x -7y = 2$$

In fact, $2-4$ is not equal to $2$.

share|cite|improve this answer

answered Apr 23 at 12:06

5xum5xum

93.2k395162

$endgroup$

share|cite|improve this answer

answered Apr 23 at 12:06

5xum5xum

93.2k395162

answered Apr 23 at 12:06

5xum5xum

93.2k395162

answered Apr 23 at 12:06

5xum5xum

93.2k395162

2

$begingroup$

The first equation simplifies to $$2x-12y=-9$$ and the second one to $$-7y-x=-2$$

share|cite|improve this answer

answered Apr 23 at 12:01

Dr. Sonnhard GraubnerDr. Sonnhard Graubner

79.6k42867

$endgroup$

add a comment | 

2

$begingroup$

The first equation simplifies to $$2x-12y=-9$$ and the second one to $$-7y-x=-2$$

share|cite|improve this answer

answered Apr 23 at 12:01

Dr. Sonnhard GraubnerDr. Sonnhard Graubner

79.6k42867

$endgroup$

add a comment | 

$begingroup$

The first equation simplifies to $$2x-12y=-9$$ and the second one to $$-7y-x=-2$$

share|cite|improve this answer

answered Apr 23 at 12:01

Dr. Sonnhard GraubnerDr. Sonnhard Graubner

79.6k42867

$endgroup$

share|cite|improve this answer

answered Apr 23 at 12:01

Dr. Sonnhard GraubnerDr. Sonnhard Graubner

79.6k42867

answered Apr 23 at 12:01

Dr. Sonnhard GraubnerDr. Sonnhard Graubner

79.6k42867

answered Apr 23 at 12:01

Dr. Sonnhard GraubnerDr. Sonnhard Graubner

79.6k42867

1

$begingroup$

Finally, we get our first simplified linear equation:
This step is wrong:

$2x-12y=-9$ this should be your first equation.

share|cite|improve this answer

answered Apr 23 at 12:02

HS SinghHS Singh

112

$endgroup$

add a comment | 

1

$begingroup$

Finally, we get our first simplified linear equation:
This step is wrong:

$2x-12y=-9$ this should be your first equation.

share|cite|improve this answer

answered Apr 23 at 12:02

HS SinghHS Singh

112

$endgroup$

add a comment | 

$begingroup$

Finally, we get our first simplified linear equation:
This step is wrong:

$2x-12y=-9$ this should be your first equation.

share|cite|improve this answer

answered Apr 23 at 12:02

HS SinghHS Singh

112

$endgroup$

share|cite|improve this answer

answered Apr 23 at 12:02

HS SinghHS Singh

112

answered Apr 23 at 12:02

HS SinghHS Singh

112

answered Apr 23 at 12:02

HS SinghHS Singh

112