Brooks Clark
11/04/2023 · Senior High School
1. Resolve aplicando o método de adição ordenada. (4.0) \( \left\{\begin{array}{l}4 x+y=7 \\ 2 x-5 y=9\end{array}\right. \) 2. Resolve aplicando o método de substituição (4.0)
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Solve the system of equations \( 4x+y=7; 2x-5y=9 \).
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
\(\left\{ \begin{array}{l}4x+y=7\\2x-5y=9\end{array}\right.\)
- step1: Solve the equation:
\(\left\{ \begin{array}{l}y=7-4x\\2x-5y=9\end{array}\right.\)
- step2: Substitute the value of \(y:\)
\(2x-5\left(7-4x\right)=9\)
- step3: Simplify:
\(22x-35=9\)
- step4: Move the constant to the right side:
\(22x=9+35\)
- step5: Add the numbers:
\(22x=44\)
- step6: Divide both sides:
\(\frac{22x}{22}=\frac{44}{22}\)
- step7: Divide the numbers:
\(x=2\)
- step8: Substitute the value of \(x:\)
\(y=7-4\times 2\)
- step9: Simplify:
\(y=-1\)
- step10: Calculate:
\(\left\{ \begin{array}{l}x=2\\y=-1\end{array}\right.\)
- step11: Check the solution:
\(\left\{ \begin{array}{l}x=2\\y=-1\end{array}\right.\)
- step12: Rewrite:
\(\left(x,y\right) = \left(2,-1\right)\)
Solve the system of equations \( 4x+y=7; 2x-5y=9 \).
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
\(\left\{ \begin{array}{l}4x+y=7\\2x-5y=9\end{array}\right.\)
- step1: Solve the equation:
\(\left\{ \begin{array}{l}y=7-4x\\2x-5y=9\end{array}\right.\)
- step2: Substitute the value of \(y:\)
\(2x-5\left(7-4x\right)=9\)
- step3: Simplify:
\(22x-35=9\)
- step4: Move the constant to the right side:
\(22x=9+35\)
- step5: Add the numbers:
\(22x=44\)
- step6: Divide both sides:
\(\frac{22x}{22}=\frac{44}{22}\)
- step7: Divide the numbers:
\(x=2\)
- step8: Substitute the value of \(x:\)
\(y=7-4\times 2\)
- step9: Simplify:
\(y=-1\)
- step10: Calculate:
\(\left\{ \begin{array}{l}x=2\\y=-1\end{array}\right.\)
- step11: Check the solution:
\(\left\{ \begin{array}{l}x=2\\y=-1\end{array}\right.\)
- step12: Rewrite:
\(\left(x,y\right) = \left(2,-1\right)\)
Solve the system of equations \( 4x+y=7; 2x-5y=9 \).
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
\(\left\{ \begin{array}{l}4x+y=7\\2x-5y=9\end{array}\right.\)
- step1: Solve the equation:
\(\left\{ \begin{array}{l}y=7-4x\\2x-5y=9\end{array}\right.\)
- step2: Substitute the value of \(y:\)
\(2x-5\left(7-4x\right)=9\)
- step3: Simplify:
\(22x-35=9\)
- step4: Move the constant to the right side:
\(22x=9+35\)
- step5: Add the numbers:
\(22x=44\)
- step6: Divide both sides:
\(\frac{22x}{22}=\frac{44}{22}\)
- step7: Divide the numbers:
\(x=2\)
- step8: Substitute the value of \(x:\)
\(y=7-4\times 2\)
- step9: Simplify:
\(y=-1\)
- step10: Calculate:
\(\left\{ \begin{array}{l}x=2\\y=-1\end{array}\right.\)
- step11: Check the solution:
\(\left\{ \begin{array}{l}x=2\\y=-1\end{array}\right.\)
- step12: Rewrite:
\(\left(x,y\right) = \left(2,-1\right)\)
Solve the system of equations \( 4x+y=7; 2x-5y=9 \).
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
\(\left\{ \begin{array}{l}4x+y=7\\2x-5y=9\end{array}\right.\)
- step1: Solve the equation:
\(\left\{ \begin{array}{l}y=7-4x\\2x-5y=9\end{array}\right.\)
- step2: Substitute the value of \(y:\)
\(2x-5\left(7-4x\right)=9\)
- step3: Simplify:
\(22x-35=9\)
- step4: Move the constant to the right side:
\(22x=9+35\)
- step5: Add the numbers:
\(22x=44\)
- step6: Divide both sides:
\(\frac{22x}{22}=\frac{44}{22}\)
- step7: Divide the numbers:
\(x=2\)
- step8: Substitute the value of \(x:\)
\(y=7-4\times 2\)
- step9: Simplify:
\(y=-1\)
- step10: Calculate:
\(\left\{ \begin{array}{l}x=2\\y=-1\end{array}\right.\)
- step11: Check the solution:
\(\left\{ \begin{array}{l}x=2\\y=-1\end{array}\right.\)
- step12: Rewrite:
\(\left(x,y\right) = \left(2,-1\right)\)
Para resolver o sistema de equações dado, utilizamos o método de substituição, o método de eliminação, o método de Gauss-Jordan e o método de Cramer. Em todos os casos, a solução do sistema de equações é \( (x, y) = (2, -1) \).
Quick Answer
A solução do sistema de equações é \( (x, y) = (2, -1) \).
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