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{:[2w-3z=-1],[3w+4z=24]:}

$25$ . $\begin{array}{l}2 w-3 z=-1 \\ 3 w+4 z=24\end{array}$

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Write an equation word problem

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Q.

25

.

\begin{array}{l}2 w-3 z=-1 \\ 3 w+4 z=24\end{array}

Set Up Equations: We have a system of linear equations: $\newline$ {\begin{array}{l}2w-3z=-1\3w+4z=24\end{array}} $\newline$ Let's use the method of substitution or elimination to solve for $w$ and $z$ . We will use the elimination method in this case.
Multiply Equations: First, we need to make the coefficients of either $w$ or $z$ the same in both equations. Let's multiply the first equation by $3$ and the second equation by $2$ to make the coefficients of $w$ the same: $\newline$ $3(2w - 3z) = 3(-1)$ $\newline$ $2(3w + 4z) = 2(24)$ $\newline$ This gives us: $\newline$ \begin{cases}6w - 9z = -3\6w + 8z = 48\end{cases}
Eliminate Variable: Now, we subtract the second equation from the first to eliminate $w$ : $(6w - 9z) - (6w + 8z) = -3 - 48$ This simplifies to: $-9z - 8z = -51$ Combining like terms, we get: $-17z = -51$
Solve for z: Next, we divide both sides by $-17$ to solve for z: $\newline$ $z = \frac{-51}{-17}$ $\newline$ $z = 3$
Substitute $z$ into Equation: Now that we have the value of $z$ , we can substitute it back into one of the original equations to solve for $w$ . Let's use the first equation: $\newline$ $2w - 3z = -1$ $\newline$ $2w - 3(3) = -1$ $\newline$ $2w - 9 = -1$
Solve for w: We add $9$ to both sides to solve for $w$ : $\newline$ $2w = -1 + 9$ $\newline$ $2w = 8$
Solve for w: We add $9$ to both sides to solve for $w$ : $\newline$ $2w = -1 + 9$ $\newline$ $2w = 8$ Finally, we divide both sides by $2$ to find $w$ : $\newline$ $w = 8 / 2$ $\newline$ $w = 4$

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