Question

Solve the system of equations using elimination: minus, 3, x, plus, y, equals, 8−3x+y=8 and minus, 4, x, plus, 2, y, equals, 4−4x+2y=4.

Answer 1

To solve the system of equations using elimination, we can multiply the first equation by 2 and the second equation by -1 to eliminate the "x" terms.

Multiplying the first equation by 2:

2(8 - 3x + y) = 2(8)
16 - 6x + 2y = 16
-6x + 2y = 0

Multiplying the second equation by -1:

-1(-4x + 2y) = -1(4)
4x - 2y = -4

Now, we can add the two equations together to eliminate the "x" term:

(-6x + 2y) + (4x - 2y) = 0 + (-4)
-6x + 4x + 2y - 2y = -4
-2x = -4
x = 2

Substituting the value of x into one of the original equations:

-3(2) + y = 8
-6 + y = 8
y = 8 + 6
y = 14

Therefore, the solution to the system of equations is x = 2 and y = 14.