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Math  /  Algebra

QuestionSolve using substitution. y=−x+2y=−4x−4\begin{array}{l} y=-x+2 \\ y=-4 x-4 \end{array}

Studdy Solution

STEP 1

1. We are given a system of two linear equations.
2. We will solve the system using the substitution method.
3. The goal is to find the values of x x and y y that satisfy both equations simultaneously.

STEP 2

1. Solve one of the equations for one variable.
2. Substitute the expression from Step 1 into the other equation.
3. Solve the resulting equation for the remaining variable.
4. Substitute back to find the other variable.
5. Verify the solution by substituting both values into the original equations.

STEP 3

Choose one of the equations to solve for one variable. The first equation is already solved for y y :
y=−x+2 y = -x + 2

STEP 4

Substitute the expression for y y from the first equation into the second equation:
−x+2=−4x−4 -x + 2 = -4x - 4

STEP 5

Solve the equation from Step 2 for x x :
Add 4x 4x to both sides:
−x+4x+2=−4 -x + 4x + 2 = -4
Simplify:
3x+2=−4 3x + 2 = -4
Subtract 2 from both sides:
3x=−6 3x = -6
Divide both sides by 3:
x=−2 x = -2

STEP 6

Substitute x=−2 x = -2 back into the expression for y y from Step 1:
y=−(−2)+2 y = -(-2) + 2
Simplify:
y=2+2=4 y = 2 + 2 = 4

STEP 7

Verify the solution by substituting x=−2 x = -2 and y=4 y = 4 into the original equations:
First equation:
y=−x+2 y = -x + 2
4=−(−2)+2 4 = -(-2) + 2
4=2+2 4 = 2 + 2
4=4 4 = 4 (True)
Second equation:
y=−4x−4 y = -4x - 4
4=−4(−2)−4 4 = -4(-2) - 4
4=8−4 4 = 8 - 4
4=4 4 = 4 (True)
Both equations are satisfied.
The solution is:
x=−2, y=4 x = -2, \, y = 4

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