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Math  /  Algebra

QuestionQuestion
Solve the system by substitution. y=−xy=−4x+12\begin{array}{l} y=-x \\ y=-4 x+12 \end{array}
Answer Attempt 1 out of 2 (□(\square □\square ) Submit Answer

Studdy Solution

STEP 1

1. We have a system of two linear equations: y=−x y = -x and y=−4x+12 y = -4x + 12 .
2. We are using the substitution method to solve this system.
3. The solution will be a point (x,y)(x, y) where both equations intersect.

STEP 2

1. Substitute the expression for y y from the first equation into the second equation.
2. Solve the resulting equation for x x .
3. Substitute the value of x x back into one of the original equations to find y y .
4. Verify the solution by checking it satisfies both original equations.

STEP 3

Substitute the expression for y y from the first equation y=−x y = -x into the second equation y=−4x+12 y = -4x + 12 :
−x=−4x+12 -x = -4x + 12

STEP 4

Solve the equation −x=−4x+12-x = -4x + 12 for x x .
First, add 4x 4x to both sides to get:
3x=12 3x = 12

STEP 5

Now, divide both sides by 3 to solve for x x :
x=4 x = 4

STEP 6

Substitute x=4 x = 4 back into the first equation y=−x y = -x to find y y :
y=−4 y = -4

STEP 7

Verify the solution (x,y)=(4,−4)(x, y) = (4, -4) by checking it in the second equation y=−4x+12 y = -4x + 12 :
Substitute x=4 x = 4 and y=−4 y = -4 :
−4=−4(4)+12 -4 = -4(4) + 12
Simplify the right-hand side:
−4=−16+12 -4 = -16 + 12
−4=−4 -4 = -4
Both sides are equal, confirming the solution is correct.
The solution to the system is:
(4,−4) (4, -4)

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