Solve the system by the elimination method
6x+2y=-16
-x-3y=-16
well first multiply the first one by 1/2
and the second one by -1
3 x + 1 y = -8
1 x + 3 y = 16
now multiply the first one by 3
9 x + 3 y =-24
1 x + 3 y = 16
-------------- subtract
8 x + 0 = -40
so
x = -5
-30 + 2y = -16
2 y = 14
y = 7
To solve the system of equations using the elimination method, we will eliminate one variable by adding the two equations together.
Let's start by multiplying the second equation by 6 to make the coefficients of x in both equations the same:
6 * (-x - 3y) = 6 * (-16)
-6x - 18y = -96
Now, we can add the two equations together to eliminate the x variable:
(6x + 2y) + (-6x - 18y) = (-16) + (-96)
(6x - 6x) + (2y - 18y) = -16 - 96
0x - 16y = -112
-16y = -112
To isolate y, divide both sides of the equation by -16:
-16y / -16 = -112 / -16
y = 7
Now that we have the value of y, we can substitute it back into either of the original equations to solve for x. Let's use the first equation:
6x + 2y = -16
6x + 2(7) = -16
6x + 14 = -16
6x = -16 - 14
6x = -30
Divide both sides of the equation by 6:
6x / 6 = -30 / 6
x = -5
The solution to the system of equations is x = -5 and y = 7.