Rodriguez Deleon
05/31/2023 · Senior High School
Resolver por IGUALACIO'N \( \left\{\begin{array}{l}x+y=2 \\ y+2 x=9\end{array}\right. \)
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Step-by-step Solution
Solve the system of equations \( \begin{cases}x+y=2\\y+2x=9\end{cases} \).
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
\(\left\{ \begin{array}{l}x+y=2\\y+2x=9\end{array}\right.\)
- step1: Solve the equation:
\(\left\{ \begin{array}{l}x=2-y\\y+2x=9\end{array}\right.\)
- step2: Substitute the value of \(x:\)
\(y+2\left(2-y\right)=9\)
- step3: Simplify:
\(-y+4=9\)
- step4: Move the constant to the right side:
\(-y=9-4\)
- step5: Subtract the numbers:
\(-y=5\)
- step6: Change the signs:
\(y=-5\)
- step7: Substitute the value of \(y:\)
\(x=2-\left(-5\right)\)
- step8: Simplify:
\(x=7\)
- step9: Calculate:
\(\left\{ \begin{array}{l}x=7\\y=-5\end{array}\right.\)
- step10: Check the solution:
\(\left\{ \begin{array}{l}x=7\\y=-5\end{array}\right.\)
- step11: Rewrite:
\(\left(x,y\right) = \left(7,-5\right)\)
La solución de las ecuaciones dadas por igualación es \( (x, y) = (7, -5) \).
Quick Answer
La solución es \( (x, y) = (7, -5) \).
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