Answer:
The y-coordinate of the solution for the system of equations is -3
Step-by-step explanation:
* Lets explain how to solve the system of equations
- We can solve the system of equations by the elimination method
# Eliminate one of the two variables by equating the coefficient of it
in the two equations with opposite signs
# Add the equations and find the value of the other variable
# Substitute its value in one of the two equations to find the
eliminated variable
* Lets solve the problem
- The system of the equations are:
∵ x - y = 12 ⇒ (1)
- Lets arrange the terms in the other equation
∵ 27 + 3y = 2x ⇒ subtract 3y from both sides
∴ 27 = 2x - 3y ⇒ switch the two sides
∴ 2x - 3y = 27 ⇒ (2)
- Multiply equation (1) by -2 to eliminate x
∴ x(-2) - y(-2) = 12(-2)
∴ -2x + 2y = -24 ⇒ (3)
- Add (2) and (3)
∵ 2x - 3y = 27 ⇒ (2)
∵ -2x + 2y = -24 ⇒ (3)
∴ -y = 3 ⇒ multiply both sides by -1
∴ y = -3
* The y-coordinate of the solution for the system of equations is -3
