Ask a New Question
Menu

solve this system.

2x-y=1
-3x+y=-5
A.(7,4)
B.(4,7)
C.(-4,7)
D.(-7,4)

1 answer

To solve the system of equations given by:

  1. \( 2x - y = 1 \) (Equation 1)
  2. \( -3x + y = -5 \) (Equation 2)

Let's solve these equations step-by-step.

From Equation 1:

  1. Rearranging for \( y \): \[ y = 2x - 1 \]

Now substitute \( y \) in Equation 2:

  1. Substitute \( y \) into Equation 2: \[ -3x + (2x - 1) = -5 \] \[ -3x + 2x - 1 = -5 \] \[ -x - 1 = -5 \] \[ -x = -5 + 1 \] \[ -x = -4 \] \[ x = 4 \]

Now substitute \( x = 4 \) back into \( y = 2x - 1 \) to find \( y \):

  1. Calculate \( y \): \[ y = 2(4) - 1 \] \[ y = 8 - 1 \] \[ y = 7 \]

Thus, the solution to the system of equations is \( (4, 7) \).

The correct answer from the options provided is:

B. (4, 7).