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Solve the system of equations.

{:[10 x-9y=24],[y=x-2],[x=◻],[y=◻]:}

Solve the system of equations. $\newline$ $\begin{array}{l} 10 x-9 y=24 \\ y=x-2 \\ x=\square \\ y=\square \end{array}$

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Solve a system of equations using substitution

Full solution

Q. Solve the system of equations.

\newline

\begin{array}{l} 10 x-9 y=24 \\ y=x-2 \\ x=\square \\ y=\square \end{array}

Substitute $y$ into first equation: Substitute $y$ from the second equation into the first equation. $\newline$ We have $y = x - 2$ . Substitute this into $10x - 9y = 24$ . $\newline$ $10x - 9(x - 2) = 24$
Simplify the equation: Distribute $-9$ to both terms in the parentheses and simplify. $\newline$ $10x - 9x + 18 = 24$ $\newline$ $x = 24 - 18$ $\newline$ $x = 6$
Solve for x: Substitute $x$ back into the second equation to find $y$ . $\newline$ $y = x - 2$ $\newline$ $y = 6 - 2$ $\newline$ $y = 4$
Substitute $x$ back into second equation: Write the solution as an ordered pair. $\newline$ The solution is $(x, y) = (6, 4)$ .

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