Solve the system by substitution: y=−2x−7 9x−10y=12
First, we need to solve one of the equations for one variable in terms of the other variable. Let's solve the first equation for x:
y = -2x - 7
We can rearrange this equation to get x in terms of y:
-2x = y + 7
x = - (y + 7)/2
Now, substitute this expression for x into the second equation:
9x - 10y = 12
9(- (y + 7)/2) - 10y = 12
-9(y + 7) - 20y = 24
-9y - 63 - 20y = 24
-29y - 63 = 24
-29y = 24 + 63
-29y = 87
y = -3
Now substitute this value for y back into the first equation to find x:
x = - (y + 7)/2
x = - ( -3 + 7)/2
x = 4/2
x = 2
Therefore, the solution to the system of equations is x = 2 and y = -3.