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Consider the following system of equations,

{:[-2x-9y=12],[-2x-7y=8]:}

Consider the following system of equations, $\newline$ $\begin{aligned} -2 x-9 y & =12 \\ -2 x-7 y & =8 \end{aligned}$

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Write an equation word problem

Full solution

Q. Consider the following system of equations,

\newline

\begin{aligned} -2 x-9 y & =12 \\ -2 x-7 y & =8 \end{aligned}

Write Equations: Step $1$ : Write down the system of equations. $\newline$ $-2x - 9y = 12$ $\newline$ $-2x - 7y = 8$
Eliminate x: Step $2$ : Subtract the second equation from the first to eliminate x. $\newline$ $(-2x - 9y) - (-2x - 7y) = 12 - 8$ $\newline$ $-2x + 2x - 9y + 7y = 4$ $\newline$ $-2y = 4$
Solve for y: Step $3$ : Solve for y. $\newline$ $-2y = 4$ $\newline$ $y = \frac{4}{-2}$ $\newline$ $y = -2$
Substitute and Solve for x: Step $4$ : Substitute $y = -2$ into the first equation to solve for x. $\newline$ $-2x - 9(-2) = 12$ $\newline$ $-2x + 18 = 12$ $\newline$ $-2x = 12 - 18$ $\newline$ $-2x = -6$ $\newline$ $x = -6 / -2$ $\newline$ $x = 3$

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