Question
Solve the system by substitution. \[ \begin{array}{l}y=6 x-24 \\ y=-2 x\end{array} \] Answer Attempt 1 out of 2
Ask by Bolton Guzman. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solution to the system is \( x = 3 \) and \( y = -6 \).
Solution
We are given the system:
y = 6x – 24
y = –2x
Step 1: Since both expressions equal y, set them equal to each other:
6x – 24 = –2x
Step 2: Solve for x.
6x + 2x = 24 (Add 2x to both sides)
8x = 24
x = 24 ÷ 8 = 3
Step 3: Substitute x = 3 back into one of the equations to find y. We'll use y = –2x:
y = –2(3) = –6
Thus, the solution to the system is:
x = 3, y = –6.
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Simplify this solution Mind Expander
To solve the system using substitution, start with the first equation, \( y = 6x - 24 \). Now substitute \( y \) in the second equation, giving us: \[ -2x = 6x - 24 \] Now, combine like terms by adding \( 2x \) to both sides: \[ 0 = 8x - 24 \] Add 24 to both sides: \[ 24 = 8x \] Dividing by 8 gives: \[ x = 3 \] Next, substitute \( x = 3 \) back into the first equation to find \( y \): \[ y = 6(3) - 24 = 18 - 24 = -6 \] Thus, the solution to the system is \( (3, -6) \).
