Question

Math

Posted 6 months ago

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

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Answer from Sia

Posted 6 months ago

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 $-8$, which gives $x = -2$

Answer

$x = -2$ and $y = -8$

Key Concept

Substitution Method for Solving Systems of Equations

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.

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