Question
6) \( \begin{aligned} 6 x+6 y & =-6 \\ -2 x-3 y & =-3\end{aligned} \)
Ask by Olson Logan. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The solution is \( x = -6 \) and \( y = 5 \).
Solution
Solve the system of equations \( 6x+6y=-6;-2x-3y=-3 \).
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
\(\left\{ \begin{array}{l}6x+6y=-6\\-2x-3y=-3\end{array}\right.\)
- step1: Solve the equation:
\(\left\{ \begin{array}{l}x=-1-y\\-2x-3y=-3\end{array}\right.\)
- step2: Substitute the value of \(x:\)
\(-2\left(-1-y\right)-3y=-3\)
- step3: Simplify:
\(2-y=-3\)
- step4: Move the constant to the right side:
\(-y=-3-2\)
- step5: Subtract the numbers:
\(-y=-5\)
- step6: Change the signs:
\(y=5\)
- step7: Substitute the value of \(y:\)
\(x=-1-5\)
- step8: Simplify:
\(x=-6\)
- step9: Calculate:
\(\left\{ \begin{array}{l}x=-6\\y=5\end{array}\right.\)
- step10: Check the solution:
\(\left\{ \begin{array}{l}x=-6\\y=5\end{array}\right.\)
- step11: Rewrite:
\(\left(x,y\right) = \left(-6,5\right)\)
The solution to the system of equations is \( (x,y) = (-6,5) \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To solve the system of equations \( 6x + 6y = -6 \) and \( -2x - 3y = -3 \), we can start by simplifying both equations. Dividing the first equation by 6 gives us \( x + y = -1 \) or \( y = -1 - x \). For the second equation, dividing by -1 yields \( 2x + 3y = 3 \). Now, substituting \( y = -1 - x \) into the second equation: \[ 2x + 3(-1 - x) = 3 \] \[ 2x - 3 - 3x = 3 \] \[ -1x - 3 = 3 \] \[ -1x = 6 \implies x = -6 \] Now substituting \( x = -6 \) back into \( y = -1 - x \): \[ y = -1 - (-6) = -1 + 6 = 5 \] Thus, the solution to the system of equations is \( x = -6 \) and \( y = 5 \). Let's express them in coordinate form: The solution is the point \( (-6, 5) \).
