Question

Solve the linear system using the SUBSTITUTION method.
-3x + y = –15 and 2x + 5y = -7.

Answer 1

To solve the given linear system using the substitution method, we first isolate y in the first equation, then substitute it into the second equation. We find that x = 4 and y = -3.

Step-by-step explanation:

To solve the linear system using the substitution method, we begin with the given equations:

• -3x + y = –15 (Equation 1)
• 2x + 5y = -7 (Equation 2)

Let's first solve Equation 1 for y:

1. y = 3x - 15

Now, we'll substitute y in Equation 2 with the expression from Equation 1:

1. 2x + 5(3x - 15) = -7
2. 2x + 15x - 75 = -7
3. 17x - 75 = -7
4. 17x = 68
5. x = 4

Next, plug the value of x into the expression for y:

1. y = 3(4) - 15
2. y = 12 - 15
3. y = -3

Therefore, the solution to the system of equations is x = 4 and y = -3.