Question

Math

Posted 3 months ago

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

Sign in to unlock the answer

Answer from Sia

Posted 3 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

Simplify the equation: $13y + 78 - 6y = 22$

step 4

Combine like terms to get $7y + 78 = 22$

step 5

Subtract 78 from both sides to get $7y = -56$

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

Solve for $x$: $x = -8 + 6$

step 9

Simplify to find $x = -2$

Answer

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

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.

Not the question you are looking for? Ask here!

Enter question by text

Enter question by image

Upgrade to Asksia Pro

Join a AskSia's Pro Plan, and get 24/7 AI tutoring for your reviews, assignments, quizzes and exam preps.

Unlimited chat query usages

Strong algorithms that better know you

Early access to new release features

Study Other Question