Question
Sinultaneous ly if \( 2 x-y=17 \quad \& \quad 4 y+3 x=9 \)
Ask by Rojas Newton. in South Africa
Mar 08,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
There are \( x=7 \) and \( y=-3 \).
Solution
Solve the system of equations \( 2x-y=17;4y+3x=9 \).
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
\(\left\{ \begin{array}{l}2x-y=17\\4y+3x=9\end{array}\right.\)
- step1: Solve the equation:
\(\left\{ \begin{array}{l}y=-17+2x\\4y+3x=9\end{array}\right.\)
- step2: Substitute the value of \(y:\)
\(4\left(-17+2x\right)+3x=9\)
- step3: Simplify:
\(-68+11x=9\)
- step4: Move the constant to the right side:
\(11x=9+68\)
- step5: Add the numbers:
\(11x=77\)
- step6: Divide both sides:
\(\frac{11x}{11}=\frac{77}{11}\)
- step7: Divide the numbers:
\(x=7\)
- step8: Substitute the value of \(x:\)
\(y=-17+2\times 7\)
- step9: Calculate:
\(y=-3\)
- step10: Calculate:
\(\left\{ \begin{array}{l}x=7\\y=-3\end{array}\right.\)
- step11: Check the solution:
\(\left\{ \begin{array}{l}x=7\\y=-3\end{array}\right.\)
- step12: Rewrite:
\(\left(x,y\right) = \left(7,-3\right)\)
The solution to the system of equations \(2x-y=17\) and \(4y+3x=9\) is \(x=7\) and \(y=-3\).
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Simplify this solution Mind Expander
To solve the simultaneous equations \( 2x - y = 17 \) and \( 4y + 3x = 9 \), we can use substitution or elimination. First, we can express \( y \) from the first equation: \[ y = 2x - 17 \] Now, substitute this expression for \( y \) into the second equation: \[ 4(2x - 17) + 3x = 9 \] Expanding this gives: \[ 8x - 68 + 3x = 9 \] Combining like terms: \[ 11x - 68 = 9 \] Now, add 68 to both sides: \[ 11x = 77 \] Dividing by 11: \[ x = 7 \] Now that we have \( x \), substitute it back into the equation for \( y \): \[ y = 2(7) - 17 = 14 - 17 = -3 \] Thus, the solution to the simultaneous equations is: \[ \boxed{(7, -3)} \]
