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Math  /  Algebra

Question2x−y=−2x=−2\begin{array}{l}2 x-y=-2 \\ x=-2\end{array}

Studdy Solution

STEP 1

1. We have a system of two linear equations: $ \begin{array}{l} 2x - y = -2 \\ x = -2 \end{array} \]
2. The goal is to find the values of \( x \) and \( y \) that satisfy both equations.
3. The second equation directly provides the value of \( x \).

STEP 2

1. Substitute the value of x x from the second equation into the first equation.
2. Solve for y y .
3. Verify the solution by substituting both values back into the original equations.

STEP 3

Substitute x=−2 x = -2 from the second equation into the first equation:
2(−2)−y=−2 2(-2) - y = -2

STEP 4

Simplify the equation:
−4−y=−2 -4 - y = -2
Add 4 to both sides to isolate y y :
−y=−2+4 -y = -2 + 4

STEP 5

Simplify further:
−y=2 -y = 2
Multiply both sides by −1-1 to solve for y y :
y=−2 y = -2

STEP 6

Verify the solution by substituting x=−2 x = -2 and y=−2 y = -2 back into the original equations:
For the first equation: 2(−2)−(−2)=−2 2(-2) - (-2) = -2 −4+2=−2 -4 + 2 = -2 −2=−2 -2 = -2
For the second equation: x=−2 x = -2
Both equations are satisfied.
The solution is: x=−2, y=−2 x = -2, \, y = -2

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