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Solve the system by substitution.

{:[y=-5x],[y=-x+4]:}

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Solve the system by substitution. $\newline$ $\begin{array}{l} y=-5 x \\ y=-x+4 \end{array}$ $\newline$ $(\square, \square)$

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Identify independent and dependent variables: word problems

Full solution

Q. Solve the system by substitution.

\newline

\begin{array}{l} y=-5 x \\ y=-x+4 \end{array}

\newline

(\square, \square)

Set Equations Equal: Set the two equations equal to each other since they both equal $y$ . $\newline$ Since $y = -5x$ and $y = -x + 4$ , we can set $-5x$ equal to $-x + 4$ .
Solve for x: Solve for x. $\newline$ $-5x = -x + 4$ $\newline$ Now, add $5x$ to both sides to get all x terms on one side. $\newline$ $-5x + 5x = -x + 4 + 5x$ $\newline$ $0 = 4x + 4$
Isolate $x$ : Isolate $x$ . $\newline$ Subtract $4$ from both sides to solve for $x$ . $\newline$ $0 - 4 = 4x + 4 - 4$ $\newline$ $-4 = 4x$
Divide to Find x: Divide both sides by $4$ to find the value of $x$ . $-\frac{4}{4} = \frac{4x}{4}$ $-1 = x$
Substitute for y: Substitute $x$ back into one of the original equations to solve for $y$ . We can use $y = -5x$ . $y = -5(-1)$ $y = 5$
Check Solution: Check the solution with the other equation. $\newline$ Substitute $x = -1$ into $y = -x + 4$ . $\newline$ $y = -(-1) + 4$ $\newline$ $y = 1 + 4$ $\newline$ $y = 5$ $\newline$ Since this matches the $y$ value we found when we substituted into the first equation, our solution is correct.

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