Valdez Sanders
04/09/2024 · Junior High School
Use substitution to solve the system \[ \begin{array}{r}2 x-9=y \\ 3 x+2 y=17\end{array} \]
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Step-by-step Solution
Solve the system of equations \( 2x-9=y;3x+2y=17 \).
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
\(\left\{ \begin{array}{l}2x-9=y\\3x+2y=17\end{array}\right.\)
- step1: Rewrite the expression:
\(\left\{ \begin{array}{l}y=2x-9\\3x+2y=17\end{array}\right.\)
- step2: Substitute the value of \(y:\)
\(3x+2\left(2x-9\right)=17\)
- step3: Simplify:
\(7x-18=17\)
- step4: Move the constant to the right side:
\(7x=17+18\)
- step5: Add the numbers:
\(7x=35\)
- step6: Divide both sides:
\(\frac{7x}{7}=\frac{35}{7}\)
- step7: Divide the numbers:
\(x=5\)
- step8: Substitute the value of \(x:\)
\(y=2\times 5-9\)
- step9: Simplify:
\(y=1\)
- step10: Calculate:
\(\left\{ \begin{array}{l}x=5\\y=1\end{array}\right.\)
- step11: Check the solution:
\(\left\{ \begin{array}{l}x=5\\y=1\end{array}\right.\)
- step12: Rewrite:
\(\left(x,y\right) = \left(5,1\right)\)
The solution to the system of equations using the substitution method is \( (x, y) = (5, 1) \).
Quick Answer
The solution is \( (x, y) = (5, 1) \).
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