Question
9) \( \begin{array}{l}5 x+y=9 \\ 10 x-7 y=-18\end{array} \)
Ask by Joseph Gray. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x = 1 \) and \( y = 4 \).
Solution
Solve the system of equations \( 5x+y=9;10x-7y=-18 \).
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
\(\left\{ \begin{array}{l}5x+y=9\\10x-7y=-18\end{array}\right.\)
- step1: Solve the equation:
\(\left\{ \begin{array}{l}y=9-5x\\10x-7y=-18\end{array}\right.\)
- step2: Substitute the value of \(y:\)
\(10x-7\left(9-5x\right)=-18\)
- step3: Simplify:
\(45x-63=-18\)
- step4: Move the constant to the right side:
\(45x=-18+63\)
- step5: Add the numbers:
\(45x=45\)
- step6: Divide both sides:
\(\frac{45x}{45}=\frac{45}{45}\)
- step7: Divide the numbers:
\(x=1\)
- step8: Substitute the value of \(x:\)
\(y=9-5\times 1\)
- step9: Substitute back:
\(y=9-5\)
- step10: Calculate:
\(y=4\)
- step11: Calculate:
\(\left\{ \begin{array}{l}x=1\\y=4\end{array}\right.\)
- step12: Check the solution:
\(\left\{ \begin{array}{l}x=1\\y=4\end{array}\right.\)
- step13: Rewrite:
\(\left(x,y\right) = \left(1,4\right)\)
The solution to the system of equations is \( x = 1 \) and \( y = 4 \).
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Simplify this solution Extra Insights
To solve the system of equations, you can use substitution or elimination. Let's use the substitution method. From the first equation, express \(y\) in terms of \(x\): \(y = 9 - 5x\) Now substitute \(y\) in the second equation: \(10x - 7(9 - 5x) = -18\) Expanding this gives: \(10x - 63 + 35x = -18\) Combining like terms results in: \(45x - 63 = -18\) Adding 63 to both sides yields: \(45x = 45\) Dividing by 45 gives: \(x = 1\) Now, substitute \(x\) back into the equation for \(y\): \(y = 9 - 5(1) = 4\) Thus, the solution is \(x = 1\) and \(y = 4\).
