Questions: x-y=3 2x-y=-1

x-y=3 2x-y=-1
Transcript text: \[ x-y=3 \] $2 x-y=-1$
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Solution

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Solution Steps

Step 1: Write down the system of equations

We are given the following system of equations: \[ \begin{cases} x - y = 3 \quad \text{(1)} \\ 2x - y = -1 \quad \text{(2)} \end{cases} \]

Step 2: Subtract equation (1) from equation (2)

Subtract equation (1) from equation (2) to eliminate \( y \): \[ (2x - y) - (x - y) = -1 - 3 \] Simplify: \[ 2x - y - x + y = -4 \] \[ x = -4 \]

Step 3: Substitute \( x = -4 \) into equation (1) to solve for \( y \)

Substitute \( x = -4 \) into equation (1): \[ -4 - y = 3 \] Solve for \( y \): \[ -y = 3 + 4 \] \[ -y = 7 \] \[ y = -7 \]

Final Answer

The solution to the system of equations is: \[ \boxed{x = -4, \quad y = -7} \]

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