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{:[-3a+5b=11],[6a+2b=26]:}

$\begin{array}{r}-3 a+5 b=11 \\ 6 a+2 b=26\end{array}$

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Write an equation word problem

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Q.

\begin{array}{r}-3 a+5 b=11 \\ 6 a+2 b=26\end{array}

Eliminate variable $a$ : Use elimination method to eliminate variable $a$ . Multiply the first equation by $2$ to align the coefficients of $a$ with the second equation. $\newline$ Calculation: $\newline$ First equation: $-3a + 5b = 11$ becomes $-6a + 10b = 22$ $\newline$ Second equation: $6a + 2b = 26$ $\newline$ Adding both equations: $(-6a + 10b) + (6a + 2b) = 22 + 26$ $\newline$ Simplification: $12b = 48$
Solve for b: Solve for b. $\newline$ Calculation: $\newline$ $12b = 48$ $\newline$ $b = \frac{48}{12}$ $\newline$ $b = 4$
Substitute to find $a$ : Substitute the value of $b$ back into one of the original equations to find $a$ . Using the first equation $-3a + 5b = 11$ . $\newline$ Calculation: $\newline$ $-3a + 5(4) = 11$ $\newline$ $-3a + 20 = 11$ $\newline$ $-3a = 11 - 20$ $\newline$ $-3a = -9$ $\newline$ $a = -9 / -3$ $\newline$ $a = 3$

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