Question
Solve the system by substitution. \[ \begin{aligned} y & =-5 x \\ y & =-7 x-14\end{aligned} \]
Ask by Stewart Perkins. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The solution is \( x = -7 \) and \( y = 35 \).
Solution
Solve the system of equations \( y=-5x;y=-7x-14 \).
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
\(\left\{ \begin{array}{l}y=-5x\\y=-7x-14\end{array}\right.\)
- step1: Substitute the value of \(y:\)
\(-5x=-7x-14\)
- step2: Move the variable to the left side:
\(-5x+7x=-14\)
- step3: Add the terms:
\(2x=-14\)
- step4: Divide both sides:
\(\frac{2x}{2}=\frac{-14}{2}\)
- step5: Divide the numbers:
\(x=-7\)
- step6: Substitute the value of \(x:\)
\(y=-5\left(-7\right)\)
- step7: Simplify:
\(y=35\)
- step8: Calculate:
\(\left\{ \begin{array}{l}x=-7\\y=35\end{array}\right.\)
- step9: Check the solution:
\(\left\{ \begin{array}{l}x=-7\\y=35\end{array}\right.\)
- step10: Rewrite:
\(\left(x,y\right) = \left(-7,35\right)\)
The solution to the system of equations by substitution is \( (x,y) = (-7,35) \).
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Beyond the Answer
To solve the system by substitution, start with the first equation: 1. From \( y = -5x \), we can substitute this expression for \( y \) into the second equation: \[ -5x = -7x - 14 \] 2. To solve for \( x \), rearrange the equation: \[ -5x + 7x = -14 \] \[ 2x = -14 \] \[ x = -7 \] 3. Now, substitute \( x = -7 \) back into the first equation to find \( y \): \[ y = -5(-7) = 35 \] Thus, the solution to the system of equations is \( (x, y) = (-7, 35) \).
