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Solve the system of equations.

{:[-5x+2y=9],[y=7x],[x=◻],[y=◻]:}

Solve the system of equations. $\newline$ $\begin{array}{l} -5 x+2 y=9 \\ y=7 x \\ x=\square \\ y=\square \end{array}$

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Solve a system of equations using substitution

Full solution

Q. Solve the system of equations.

\newline

\begin{array}{l} -5 x+2 y=9 \\ y=7 x \\ x=\square \\ y=\square \end{array}

Substitute $y = 7x$ : Substitute $y = 7x$ into the first equation. $\newline$ We have the system of equations: $\newline$ $-5x + 2y = 9$ $\newline$ $y = 7x$ $\newline$ Substitute $7x$ for $y$ in the first equation: $\newline$ $-5x + 2(7x) = 9$
Simplify and solve for x: Simplify the equation and solve for x. $\newline$ $-5x + 14x = 9$ $\newline$ Combine like terms: $\newline$ $9x = 9$ $\newline$ Divide both sides by $9$ to isolate $x$ : $\newline$ $x = \frac{9}{9}$ $\newline$ $x = 1$
Substitute $x = 1$ into $y = 7x$ : Substitute $x = 1$ into $y = 7x$ to find $y$ .
$y = 7(1)$
$y = 7$
Write the solution as an ordered pair: Write the solution as an ordered pair. $\newline$ We found: $\newline$ $x = 1$ $\newline$ $y = 7$ $\newline$ The solution in the form of an ordered pair is $(1, 7)$ .

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