Question
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Answer
\( x=5 \) and \( y=-2 \).
Solution
Solve the system of equations \( 7x-3y=41;3x-y=17 \).
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
\(\left\{ \begin{array}{l}7x-3y=41\\3x-y=17\end{array}\right.\)
- step1: Solve the equation:
\(\left\{ \begin{array}{l}7x-3y=41\\y=-17+3x\end{array}\right.\)
- step2: Substitute the value of \(y:\)
\(7x-3\left(-17+3x\right)=41\)
- step3: Simplify:
\(-2x+51=41\)
- step4: Move the constant to the right side:
\(-2x=41-51\)
- step5: Subtract the numbers:
\(-2x=-10\)
- step6: Change the signs:
\(2x=10\)
- step7: Divide both sides:
\(\frac{2x}{2}=\frac{10}{2}\)
- step8: Divide the numbers:
\(x=5\)
- step9: Substitute the value of \(x:\)
\(y=-17+3\times 5\)
- step10: Calculate:
\(y=-2\)
- step11: Calculate:
\(\left\{ \begin{array}{l}x=5\\y=-2\end{array}\right.\)
- step12: Check the solution:
\(\left\{ \begin{array}{l}x=5\\y=-2\end{array}\right.\)
- step13: Rewrite:
\(\left(x,y\right) = \left(5,-2\right)\)
The solution to the system of equations \(7x-3y=41\) and \(3x-y=17\) is \(x=5\) and \(y=-2\).
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Simplify this solution The Deep Dive
To solve the system of equations \( 7x - 3y = 41 \) and \( 3x - y = 17 \), you can use substitution or elimination. Let's use elimination here! First, solve the second equation for \( y \): \( y = 3x - 17 \). Now, substitute this expression for \( y \) into the first equation. You'll reduce it to one variable, making it much simpler to solve. Keep it organized, and soon you'll find the values of \( x \) and \( y \)! Once you have your solutions, you can check your work by plugging the values back into both original equations to ensure they satisfy both. This is a fantastic way to double-check your results and confirm your skills in algebra are sharp!
