Question

Solve the system of equations using elimination.

2x + y = 9
8x – 2y = 6

Answer 1

To solve the system of equations using elimination, we want to eliminate one variable by adding or subtracting the equations.

To eliminate the y variable, we need to multiply the first equation by 2. This will make the y term in the first equation cancel out when we add it to the second equation.

2x + y = 9
8x – 2y = 6

Multiplying the first equation by 2:
4x + 2y = 18

Now we can add the two equations together:
(4x + 2y) + (8x - 2y) = 18 + 6
12x = 24

Divide both sides by 12 to solve for x:
x = 2

Substitute this value back into one of the original equations to solve for y. Let's use the first equation:
2(2) + y = 9
4 + y = 9
y = 5

Therefore, the solution to the system of equations is x = 2 and y = 5.