At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Ask your questions and receive detailed answers from professionals with extensive experience in various fields. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

Find the solution to the system of equations.

You can use the interactive graph below to find the solution.

[tex]\[
\begin{array}{l}
\left\{
\begin{array}{l}
-7x - 2y = 14 \\
6x + 6y = 18
\end{array}
\right.
\end{array}
\][/tex]

[tex]\[ x = \square \][/tex]

[tex]\[ y = \square \][/tex]


Sagot :

Sure, let's solve this system of linear equations step by step.

We are given the system of equations:

[tex]\[ \begin{cases} -7x - 2y = 14 \\ 6x + 6y = 18 \end{cases} \][/tex]

### Step 1: Simplify the Equations if Possible
First, we’ll simplify the second equation:

[tex]\[ 6x + 6y = 18 \][/tex]

Divide every term by 6:

[tex]\[ x + y = 3 \quad \text{(Equation 2)} \][/tex]

### Step 2: Use Substitution or Elimination
We can use the substitution method here. Express [tex]\(y\)[/tex] from Equation 2:

[tex]\[ y = 3 - x \quad \text{(Equation 3)} \][/tex]

### Step 3: Substitute into the First Equation
Now, substitute Equation 3 into the first equation:

[tex]\[ -7x - 2(3 - x) = 14 \][/tex]

Simplify this equation:

[tex]\[ -7x - 6 + 2x = 14 \][/tex]

Combine like terms:

[tex]\[ -5x - 6 = 14 \][/tex]

Add 6 to both sides:

[tex]\[ -5x = 20 \][/tex]

Divide both sides by -5:

[tex]\[ x = -4 \][/tex]

### Step 4: Substitute [tex]\(x\)[/tex] Back into Equation 3
Now, substitute [tex]\(x = -4\)[/tex] back into Equation 3:

[tex]\[ y = 3 - (-4) \][/tex]

Simplify:

[tex]\[ y = 3 + 4 \\ y = 7 \][/tex]

### Step 5: Write the Solution
Therefore, the solution to the system of equations is:

[tex]\[ x = -4 \][/tex]
[tex]\[ y = 7 \][/tex]

We can now fill in the blanks:

[tex]\[ x = -4 \][/tex]
[tex]\[ y = 7 \][/tex]

This means the solution to the system of equations is [tex]\((-4, 7)\)[/tex].