How to solve 4x-5y=4 2x+y=-12

Question

I need help.

Answer 1

4x - 5y = 4                        eq. 1

 

2x + y = -12                      eq. 2

 

multiply eq. 2 by -2 and and to eq. 1:

 

 4x - 5y = 4

-4x - 2y = 24

      -7y = 28

 

y = -4

 

substitute y = -4 into eq. 1

 

4x - 5(-4) = 4

 

4x + 20 = 4

 

4x = -16

 

x = - 4

 

so, x= -4, y = -4

 

 

      

 

 

 

Answer 2

4x -5y = 4

2x + y = -12

 

Let's use elimination of the y-variable.  Multiply 2x + y = -12 by 5:

 

5*[2x + y = -12]

10x + 5y = -60

 

Now add this new equation to the first equation:

 

 4x  -  5y = 4

10x + 5y = -60

-----------------

14x +  0 = -56          [the y-variable is eliminated]

 

14x = -56

x = -4

 

To find y, plug x=-4 into either original equation:

 

2x + y = -12

2*(-4) + y = -12

-8 + y = -12

y = -4

 

The solution is (-4,-4)

 

Check:

4x- 5y = 4

4(-4) - 5(-4) = 4

-16 + 20 = 4

4 = 4          Check!

 

2x + y = -12

2(-4) + (-4) = -12

-4 - 4 = -12

-12 = -12   Check!