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Solve the system by substitution.

{:[y=-2x],[y=5x+7]:}

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Solve the system by substitution. $\newline$ $\begin{array}{l} y=-2 x \\ y=5 x+7 \end{array}$ $\newline$ $(\square, \square)$

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Identify independent and dependent variables: word problems

Full solution

Q. Solve the system by substitution.

\newline

\begin{array}{l} y=-2 x \\ y=5 x+7 \end{array}

\newline

(\square, \square)

Set Equations Equal: Set the two equations equal to each other since they both equal $y$ . $\newline$ Since $y = -2x$ and $y = 5x + 7$ , we can set $-2x$ equal to $5x + 7$ .
Solve for x: Solve for x. $\newline$ $-2x = 5x + 7$ $\newline$ Add $2x$ to both sides to get all x terms on one side: $\newline$ $-2x + 2x = 5x + 2x + 7$ $\newline$ $0 = 7x + 7$ $\newline$ Subtract $7$ from both sides: $\newline$ $-7 = 7x$ $\newline$ Divide both sides by $7$ : $\newline$ $-\frac{7}{7} = x$ $\newline$ $x = -1$
Substitute $x$ for $y$ : Substitute $x$ back into one of the original equations to solve for $y$ . We can use $y = -2x$ . $y = -2(-1)$ $y = 2$
Write Ordered Pair: Write the solution as an ordered pair. $\newline$ The solution to the system of equations is $(x, y) = (-1, 2)$ .

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