Certainly! Let's solve the given system of linear equations step-by-step.
The system of equations is:
[tex]\[
\begin{array}{l}
x + y = 11 \\
5x - y = 10
\end{array}
\][/tex]
### Step 1: Write the equations in standard form
Our given equations are already in standard form:
1. [tex]\(x + y = 11\)[/tex]
2. [tex]\(5x - y = 10\)[/tex]
### Step 2: Use the method of substitution or elimination
#### Using the Elimination Method:
1. Add the two equations to eliminate [tex]\(y\)[/tex]:
[tex]\[
(x + y) + (5x - y) = 11 + 10
\][/tex]
Simplifying this gives:
[tex]\[
x + y + 5x - y = 21
\][/tex]
[tex]\[
6x = 21
\][/tex]
Solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{21}{6}
\][/tex]
[tex]\[
x = 3.5
\][/tex]
2. Substitute [tex]\(x = 3.5\)[/tex] back into the first equation to solve for [tex]\(y\)[/tex]:
[tex]\[
x + y = 11
\][/tex]
[tex]\[
3.5 + y = 11
\][/tex]
Subtract 3.5 from both sides:
[tex]\[
y = 11 - 3.5
\][/tex]
[tex]\[
y = 7.5
\][/tex]
### Conclusion:
The solution to the system of equations is [tex]\(x = 3.5\)[/tex] and [tex]\(y = 7.5\)[/tex]. Thus, the point [tex]\((x, y) = (3.5, 7.5)\)[/tex] satisfies both equations.
So, the correct answer is:
[tex]\[
(3.5, 7.5)
\][/tex]
