Question

systems of equations
y = 2x - 1
x - y = 3
what is the value of y in the solution?

Explanation:

Step1: Substitute \( y = 2x - 1 \) into \( x - y = 3 \)

We know \( y = 2x - 1 \), so replace \( y \) in the second equation. The second equation \( x - y = 3 \) becomes \( x - (2x - 1) = 3 \).

Step2: Simplify the equation

Simplify \( x - (2x - 1) = 3 \). First, distribute the negative sign: \( x - 2x + 1 = 3 \). Then combine like terms: \( -x + 1 = 3 \). Subtract 1 from both sides: \( -x = 3 - 1 \), so \( -x = 2 \). Multiply both sides by -1: \( x = -2 \).

Step3: Find the value of \( y \)

Now that we have \( x = -2 \), substitute \( x \) into \( y = 2x - 1 \). So \( y = 2(-2) - 1 \). Calculate \( 2(-2) = -4 \), then \( y = -4 - 1 = -5 \).

Answer:

\( y = -5 \)