One way to solve a system of equations by elimination is to add or subtract the equations in such a way that one variable is eliminated. Here's one way to use elimination to solve the system of equations:
-y - 10 = 6x
5x + y = -10
First, we can add or subtract the equations in such a way that one variable is eliminated.
Add the equations :
-y - 10 + 5x + y = 6x + -10
5x = -20
x = -4
now we have x = -4 we can substitute this value in any of the equations we have.
let's substitute x = -4 in the first equation
-y -10 = 6*(-4)
-y = -40
y = 40
we have x = -4 and y = 40
we could check the solution by substitute x = -4 and y = 40 in the second equation
5*(-4) + 40 = -10
and we get 20+40 = -10, which is true.
therefore the solution for the system of equations is x = -4, y = 40