Question

Solve the system of equations: −5x = y − 5 and −2y = −x − 21. What is the solution?

a) (10, -45)
b) (-1, 10)
c) (10, 16)
d) (-1, -23)

Answer 1

To solve the system of equations, we first solve Equation 1 for y, and then substitute this value into Equation 2. Simplifying gives us the solution (-1, 10).

Step-by-step explanation:

To solve the system of equations:

• Equation 1: -5x = y - 5
• Equation 2: -2y = -x - 21

We can start by solving Equation 1 for y:

• By adding 5x to both sides, we get y = -5x + 5

Next, we substitute this value of y into Equation 2:

• -2(-5x + 5) = -x - 21

Simplifying gives 10x - 10 = -x - 21

Combining like terms, we get 11x = -11

Dividing by 11 gives x = -1

Substituting this value of x back into Equation 1 gives y = -5(-1) + 5 = 10

Therefore, the solution to the system of equations is (-1, 10).