solving by linear combination

Question

4X+3y=-10

2X+y=4

Answer 1

x - 4y = 14
3x - 4y = -6

 

Multiply the first equation by -1:

 

-1*(x - 4y = 14)

-x + 4y = -14

 

Now add this to the second equation to eliminate the y terms:

 

-x + 4y = -14

3x - 4y =   -6

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2x + 0 = -20

 

2x = -20

x = -10

 

Find y:

-x + 4y = -14

-(-10) + 4y = -14

10 + 4y = -14

4y = -24

y = -6

 

 

The solution is (-10,-6).

 

Check:

x - 4y = 14

-10 - 4(-6) = 14

-10 + 24 = 14

14 = 14     Check!

 

3x - 4y = -6

3(-10) - 4(-6) = -6

-30 + 24 = -6

-6 = -6     Check!

 

Answer 2

Multiply the top equation by -1.  so then you will have -x+4y=-14.  Add this equation to the second equation. your answer will then be 2x = -20.  (4x and -4x cancel out) divide both sides by 2, so x = -10.  Plug -10 into x.  so then you will have -10-4y=14.  Add 10 to both sides.  -4y = 24.  divide both sides by -4. so y = -6. Solution to the system of equations is (-10,-6)

 

Answer 3

The y-terms are the same, so subtract one equation from the other: 3X - X = 2X, -4Y - (-4Y) = 0, -6 - 14 = -20.

This gives a simplified system of 2X = -20.