Linear equations

Question

Given the Linear equations: 2x +3y=10. And 4x-6y=-28

 

solve for (x,y) if there is a solution

Answer 1

So, we need either the x's or y's to be opposites so that they add to 0 and cancel out.

 

Let's multiply the first equation by -2.

 

-4x - 6y = -20

4x - 6y = -28

 

Adding the two together...

 

-12y = -48

y = 4

 

2x + 3(4) = 10

2x + 12 = 10

2x = -2

x = -1

 

(-1,4)

 

Let's check.

 

2(-1) + 3(4) = 10

-2 + 12 = 10

10 = 10

0 = 0

 

4(-1) - 6(4) = -28

-4 - 24 = -28

-28 = -28

0 = 0

 

Check.