Question
(b) \( \begin{array}{l}\text { Solve: } \\ 0=-3 x+21+9 y \\ y=12 x+21\end{array} \)
Ask by Valdez Bates. in the United States
Dec 14,2024
Real Tutor Solution
Tutor-Verified Answer
Answer
The solution is \( (x, y) = (-2, -3) \).
Solution
Solve the system of equations \( -3x+21+9y=0;y=12x+21 \).
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
\(\left\{ \begin{array}{l}-3x+21+9y=0\\y=12x+21\end{array}\right.\)
- step1: Substitute the value of \(y:\)
\(-3x+21+9\left(12x+21\right)=0\)
- step2: Simplify:
\(105x+210=0\)
- step3: Move the constant to the right side:
\(105x=0-210\)
- step4: Remove 0:
\(105x=-210\)
- step5: Divide both sides:
\(\frac{105x}{105}=\frac{-210}{105}\)
- step6: Divide the numbers:
\(x=-2\)
- step7: Substitute the value of \(x:\)
\(y=12\left(-2\right)+21\)
- step8: Simplify:
\(y=-3\)
- step9: Calculate:
\(\left\{ \begin{array}{l}x=-2\\y=-3\end{array}\right.\)
- step10: Check the solution:
\(\left\{ \begin{array}{l}x=-2\\y=-3\end{array}\right.\)
- step11: Rewrite:
\(\left(x,y\right) = \left(-2,-3\right)\)
The solution to the system of equations is \( (x, y) = (-2, -3) \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To solve the system of equations, start by substituting the expression for \( y \) from the second equation into the first equation. This gives us: \[ 0 = -3x + 21 + 9(12x + 21) \] Now, simplify the right side: \[ 0 = -3x + 21 + 108x + 189 \] \[ 0 = 105x + 210 \] Next, solve for \( x \): \[ 105x = -210 \quad \Rightarrow \quad x = -2 \] Now substitute \( x = -2 \) back into the second equation to find \( y \): \[ y = 12(-2) + 21 = -24 + 21 = -3 \] Thus, the solution to the system of equations is \( x = -2 \) and \( y = -3 \).
