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{:[-2x-9y=-25],[-4x-9y=-23]:}

$\begin{aligned}-2 x-9 y & =-25 \\ -4 x-9 y & =-23\end{aligned}$

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Write an equation word problem

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Q.

\begin{aligned}-2 x-9 y & =-25 \\ -4 x-9 y & =-23\end{aligned}

Write Equations: Let's start by writing down the system of equations: $\newline$ $1$ ) $-2x - 9y = -25$ $\newline$ $2$ ) $-4x - 9y = -23$ $\newline$ We will use the method of elimination to solve this system. First, we look for a way to eliminate one of the variables by combining the equations.
Eliminate Variable: We notice that the coefficients of $y$ in both equations are the same but with opposite signs. To eliminate $y$ , we can subtract the second equation from the first one: $\newline$ $(-2x - 9y) - (-4x - 9y) = -25 - (-23)$
Simplify Equation: Performing the subtraction, we get: $\newline$ $-2x + 4x - 9y + 9y = -25 + 23$ $\newline$ This simplifies to: $\newline$ $2x = -2$
Solve for x: Now, we divide both sides of the equation by $2$ to solve for $x$ : $\newline$ $\frac{2x}{2} = \frac{-2}{2}$ $\newline$ This gives us: $\newline$ $x = -1$
Substitute $x$ : With the value of $x$ found, we can substitute it back into one of the original equations to find the value of $y$ . We'll use the first equation: $\newline$ $-2(-1) - 9y = -25$
Solve for y: Solving for y, we get: $\newline$ $2 - 9y = -25$ $\newline$ Now, we subtract $2$ from both sides: $\newline$ $-9y = -25 - 2$ $\newline$ $-9y = -27$
Final Result: Finally, we divide both sides by $-9$ to find the value of $y$ : $\frac{-9y}{-9} = \frac{-27}{-9}$ This gives us: $y = 3$

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