Solve the system by substitution.
y, equals, minus, 2, x, minus, 7
y=
−2x−7
9, x, minus, 10, y, equals, 12
9x−10y=
12
To solve the system by substitution, we will solve one of the equations for one variable and substitute it into the other equation.
We can start with the first equation: y = -2x - 7.
We will solve this equation for y:
y = -2x - 7.
Next, we will substitute this value of y into the second equation: 9x - 10y = 12.
Substituting, we get:
9x - 10(-2x - 7) = 12.
Simplifying, we get:
9x + 20x + 70 = 12.
Combining like terms, we get:
29x + 70 = 12.
Subtracting 70 from both sides, we get:
29x = -58.
Dividing by 29, we get:
x = -2.
Now that we have the value of x, we can substitute it back into one of the original equations to solve for y. Let's use the first equation: y = -2x - 7.
Substituting x = -2, we get:
y = -2(-2) - 7,
y = 4 - 7,
y = -3.
Therefore, the solution to the system is x = -2 and y = -3.