Question

Solve the system of equations using elimination/combinations-2x -y = -4 x + 2y =5

Answer 1

Answer:

x = 1, y = 2

Step-by-step explanation:

In the elimination method to solve a system of linear equations, one of the two equations is added/subtracted to the other, in order to eliminate one variable from the equation.

In this problem, we have the following two equations:

$-2x-y=-4\\x+2y=5$

To solve the system, first we multiply by 2 both sides of the second equation, and we get:

$2(x+2y)=2(5)\\2x+4y=10$

So now the system is

$-2x-y=-4\\2x+4y=10$

Now we add the two equations, and we get:

$(-2x+2x)+(-y+4y)=(-4+10)\\3y=6$

So, we get

$y=\frac{6}{3}=2$

Now we can substitute this value of y into the eq.(2), and we get:

$x+2y=5\\x+2(2)=5\\x+4=5\\x=5-4=1$