4x-2y=-6 x-1/2y=3

Question

What is the answer to this question 

 

3x+2y=11 

2x+6y=-2

Answer 1

Hi Nathan,

 

To answer the question, I will label each of the equations

 

3x+2y=11 -----eqn 1

2x+6y=-2 ----- eqn 2

 

Now pick one of the equations and make one of the variables (x or y), the subject of the equation. So let's take equation 2 and make x the subject

 

2x+6y=-2      (subtract 6y from both sides of the equation so that 2x stands alone)

2x+6y-6y=-2-6y

2x=-2-6y       (now divide both sides of the equation by 2 to make x the subject of the equation)

2x/2=-2/2 -6y/2

x=-1-3y         (at this point we will substitute x=-1-3y into either eqn 1 or 2 in order to get a solution for y)

 

Substitute -1-3y for x in eqn 1

3(-1-3y) + 2y=11     (open the brackets)

-3 - 9y + 2y =11

-3 -7y =11               (by adding liked terms -9y+2y =-7y)

-3+3 -7y =11+3       (add 3 to each side of the equation)

-7y=14                    (divide both sides of the equation by -7 to find solution for y)

-7y/-7 = 14/-7

y=-2

 

Now that we know y= -2, we can substitute it into eqn 2 to find x

 

2x+6y=-2               (substitute -2 for y)

2x+6(-2)=-2

2x-12=-2                (add 12 to both sides of the equation)

2x-12+12=-2+12

2x=10                    (divide both sides of the equation by 2)

2x/2=10/2

x=5

 

So x=5 and y=-2. To prove our answer is right, we can substitute x for 5 and y for -2 in any of our eqn. Lets take eqn. 1

 

3x+2y=11

3(5)+2(-2)=11

15-4=11

11=11   (this statement is true, 11=11 and that's how we know x=5 and y=-2)

 

I hope this helps