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 ⋮ Distribute $13$ to both terms inside the parentheses to obtain $13y + 78 - 6y = 22$. ‖ ‖ step 4 ⋮ Combine like terms to get $7y + 78 = 22$. ‖ ‖ step 5 ⋮ Subtract $78$ from both sides to isolate the term with $y$, resulting in $7y = -56$. ‖ ‖ step 6 ⋮ Divide both sides by $7$ to solve for $y$, yielding $y = -8$. ‖ ‖ step 7 ⋮ Substitute $y = -8$ back into the second equation $x = y + 6$ to find $x$. ‖ ‖ step 8 ⋮ Calculate $x$ by adding $6$ to $y$, which gives $x = -8 + 6$. ‖ ‖ step 9 ⋮ Simplify to find $x = -2$. ‖ ∻Answer∻ ⚹ $x = -2$, $y = -8$ ⚹ ∻Key Concept∻ ⚹Substitution Method⚹ ∻Explanation∻ ⚹To solve a system of equations where one equation is already solved for a variable, substitute that expression into the other equation to find the value of the remaining variable. Then, use the value found to solve for the initial variable.⚹◊What is the value of $x$ when $y=16$ in the system of equations provided by the student?⍭ Generate me a similar question◊

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