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Consider the following system of equations,

{:[-2x-9y=12],[-2x-7y=8]:}
The value of
x is

Consider the following system of equations, $\newline$ $\begin{array}{l} -2 \mathrm{x}-9 \mathrm{y}=12 \\ -2 \mathrm{x}-7 \mathrm{y}=8 \end{array}$ $\newline$ The value of $x$ is

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Which word problem matches the one-step equation?

Full solution

Q. Consider the following system of equations,

\newline

\begin{array}{l} -2 \mathrm{x}-9 \mathrm{y}=12 \\ -2 \mathrm{x}-7 \mathrm{y}=8 \end{array}

\newline

The value of

x

is

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

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