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Solve the following system of equations:

[tex]\[
\begin{array}{l}
3x - y = 11 \\
6x - 3y = 18
\end{array}
\][/tex]

A. Yes
B. No



Answer :

GinnyAnswer
To solve the system of linear equations:

1. [tex]\(3x - y = 11\)[/tex]
2. [tex]\(6x - 3y = 18\)[/tex]

we can approach it step-by-step as follows:

1. First equation:

[tex]\[ 3x - y = 11 \quad \text{(Equation 1)} \][/tex]

2. Second equation:

[tex]\[ 6x - 3y = 18 \quad \text{(Equation 2)} \][/tex]

3. We can simplify Equation 2 by dividing every term by 3:

[tex]\[ \frac{6x}{3} - \frac{3y}{3} = \frac{18}{3} \][/tex]

Simplifying, we get:

[tex]\[ 2x - y = 6 \quad \text{(Simplified Equation 2)} \][/tex]

4. Now, we have a new system of equations:

- [tex]\(3x - y = 11\)[/tex]
- [tex]\(2x - y = 6\)[/tex]

5. To eliminate [tex]\(y\)[/tex], we subtract the second equation from the first:

[tex]\[ (3x - y) - (2x - y) = 11 - 6 \][/tex]

Simplifying this, we get:

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

6. With [tex]\(x = 5\)[/tex], we substitute this value back into one of our simplified equations to find [tex]\(y\)[/tex]. Let's use [tex]\(2x - y = 6\)[/tex]:

[tex]\[ 2(5) - y = 6 \][/tex]

Simplifying:

[tex]\[ 10 - y = 6 \][/tex]

Solving for [tex]\(y\)[/tex]:

[tex]\[ y = 10 - 6 \][/tex]

[tex]\[ y = 4 \][/tex]

Thus, the solution to the system of equations is:

[tex]\[ \boxed{x = 5, y = 4} \][/tex]

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