Solve the following linear equation using the elimination method.
a. 2x + 5y = -10
-2x + 4y = 0
b. -1x - 4y = 3
5x + 2y = 3
a.
First, multiply the first equation by 2 to eliminate x:
4x + 10y = -20
-2x + 4y = 0
Now, add the two equations together:
4x + 10y + (-2x + 4y) = -20 + 0
2x + 14y = -20
Divide the equation by 2 to solve for y:
y = -20/14
y = -10/7
Now plug y back into either of the original equations to solve for x:
2x + 5(-10/7) = -10
2x - 50/7 = -10
2x = -10 + 50/7
2x = -70/7 + 50/7
2x = -20/7
x = -10/7
Therefore, the solution to the system of equations is x = -10/7, y = -10/7.
b.
First, multiply the first equation by 5 and the second equation by -1 to eliminate x:
-5x - 20y = 15
5x + 2y = 3
Now, add the two equations together:
-5x - 20y + 5x + 2y = 15 + 3
-18y = 18
y = 18 / -18
y = -1
Now plug y back into one of the original equations to solve for x:
-1x - 4(-1) = 3
-1x + 4 = 3
-1x = 3 - 4
-1x = -1
x = 1
Therefore, the solution to the system of equations is x = 1, y = -1.