Pregunta
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\( x=3 \) and \( y=-4 \).
Solución
Solve the system of equations \( -7x-2y=-13;x-2y=11 \).
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
\(\left\{ \begin{array}{l}-7x-2y=-13\\x-2y=11\end{array}\right.\)
- step1: Solve the equation:
\(\left\{ \begin{array}{l}-7x-2y=-13\\x=11+2y\end{array}\right.\)
- step2: Substitute the value of \(x:\)
\(-7\left(11+2y\right)-2y=-13\)
- step3: Simplify:
\(-77-16y=-13\)
- step4: Move the constant to the right side:
\(-16y=-13+77\)
- step5: Add the numbers:
\(-16y=64\)
- step6: Change the signs:
\(16y=-64\)
- step7: Divide both sides:
\(\frac{16y}{16}=\frac{-64}{16}\)
- step8: Divide the numbers:
\(y=-4\)
- step9: Substitute the value of \(y:\)
\(x=11+2\left(-4\right)\)
- step10: Simplify:
\(x=3\)
- step11: Calculate:
\(\left\{ \begin{array}{l}x=3\\y=-4\end{array}\right.\)
- step12: Check the solution:
\(\left\{ \begin{array}{l}x=3\\y=-4\end{array}\right.\)
- step13: Rewrite:
\(\left(x,y\right) = \left(3,-4\right)\)
The solution to the system of equations is \( (x,y) = (3,-4) \).
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución The Deep Dive
Let's take a fun little detour into the world of solving systems of equations! One way to tackle this system is by using substitution or elimination. For example, you can solve the second equation for \(x\): \( x = 2y + 11 \). Plugging that into the first equation helps you uncover the mysterious values of \(x\) and \(y\). Did you know that systems of equations date back to ancient times? Mathematicians in ancient Egypt and China used methods quite similar to those we employ today. They aimed to solve problems involving land measurements and trade, laying the groundwork for much of modern algebra!
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