Solve the system of equations.
$$
\begin{array}{l}
13 x-6 y=22 \
x=y+6 \
x=\square \
y=\square
\end{array}
$$

Question

Solve the system of equations.
$$
\begin{array}{l}
13 x-6 y=22 \
x=y+6 \
x=\square \
y=\square
\end{array}
$$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Substitute the second equation $x = y + 6$ into the first equation $13x - 6y = 22$. ‖ ‖ step 2 ⋮ Replace $x$ with $y + 6$ in the first equation to get $13(y + 6) - 6y = 22$. ‖ ‖ step 3 ⋮ Simplify the equation: $13y + 78 - 6y = 22$. ‖ ‖ step 4 ⋮ Combine like terms: $7y + 78 = 22$. ‖ ‖ step 5 ⋮ Subtract 78 from both sides: $7y = -56$. ‖ ‖ step 6 ⋮ Divide both sides by 7 to solve for $y$: $y = -8$. ‖ ‖ step 7 ⋮ Substitute $y = -8$ back into the second equation $x = y + 6$ to find $x$. ‖ ‖ step 8 ⋮ Calculate $x$: $x = -8 + 6$. ‖ ‖ step 9 ⋮ Simplify to find the value of $x$: $x = -2$. ‖ ∻Answer∻ ⚹ $x = -2$, $y = -8$ ⚹ ∻Key Concept∻ ⚹Substitution Method⚹ ∻Explanation∻ ⚹To solve a system of equations where one equation is already solved for one variable, substitute that expression into the other equation and solve for the remaining variable. Then use the found value to solve for the first variable.⚹◊What are the values of x and y that satisfy the system of equations: $$ \begin{array}{l} 13x - 6y = 22 \ x = y + 6 \end{array} $$⍭ Generate me a similar question◊

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