Final answer:
To solve the system of equations -4x + 6y = -18 and y = -2x + 21, we can substitute the value of y from the second equation into the first equation. The solution to the system of equations is x = 9 and y = 3.
Step-by-step explanation:
To solve the system of equations -4x + 6y = -18 and y = -2x + 21, we can substitute the value of y from the second equation into the first equation.
Substituting y = -2x + 21 in -4x + 6y = -18, we get -4x + 6(-2x + 21) = -18.
Simplifying this equation, we have -4x - 12x + 126 = -18. Combining like terms, we get -16x + 126 = -18.
Further simplifying, we have -16x = -18 - 126, which gives -16x = -144. Finally, dividing both sides by -16, we get x = 9. Substituting this value of x back into y = -2x + 21, we get y = -2(9) + 21 = 3.
Therefore, the solution to the system of equations is x = 9 and y = 3.