Question

A: 2x + 8y = 5 B: x + 9y = 10 To solve this system of equations by elimination, what could you multiply equation B by if you want to add the equations together and have a resulting equation with only the y-variable (the x-variable is eliminated)?

Answer 1

Ans: multiply by -2

A: 2x + 8y = 5
B: x + 9y = 10
B x (-2) : -2x - 18y = -20

A + B:
8y - 18y = 5 - 20
- 10y = -15
y = 1.5

To solve for x
B: x + 9y = 10
x + 9(1.5) = 10
x + 13.5 = 10
x = 10 - 13.5
x = -3.5

Answer 2

A: 2x + 8y = 5
B: x + 9y = 10

You can multiply equation B by -2 to be able to eliminate the x variable in both equations when you add them together.
B) -2(x + 9y)= 10
-2x - 18y= -20

Add both equations together:
2x + 8y = 5
+(-2x - 18y= -20 )
the x variable is eliminated
-10y= -15
divide both sides by -10
y= -15/-10
y= 1 1/2

Solve for x:
x + 9y= 10
x + 9(1 1/2)= 10
x + 13.5= 10
x= -3.5

ANSWER: multiply equation B by -2

Hope this helps! :)