To determine if the point [tex]\((2,3)\)[/tex] is a solution to the system of linear equations:
[tex]\[
\begin{array}{l}
y = 2x - 1 \\
y = x + 1
\end{array}
\][/tex]
we need to check if substituting [tex]\(x = 2\)[/tex] and [tex]\(y = 3\)[/tex] into both equations makes them true.
1. Check the first equation: [tex]\(y = 2x - 1\)[/tex]
Substitute [tex]\(x = 2\)[/tex] and [tex]\(y = 3\)[/tex]:
[tex]\[
3 = 2(2) - 1
\][/tex]
Simplify the right side:
[tex]\[
3 = 4 - 1
\][/tex]
[tex]\[
3 = 3
\][/tex]
This equation is satisfied.
2. Check the second equation: [tex]\(y = x + 1\)[/tex]
Substitute [tex]\(x = 2\)[/tex] and [tex]\(y = 3\)[/tex]:
[tex]\[
3 = 2 + 1
\][/tex]
Simplify the right side:
[tex]\[
3 = 3
\][/tex]
This equation is also satisfied.
Since both equations are satisfied when [tex]\(x = 2\)[/tex] and [tex]\(y = 3\)[/tex], the point [tex]\((2,3)\)[/tex] satisfies the system of linear equations.
Therefore, the statement:
[tex]$(2,3)$[/tex] is a solution to the following system of linear equations:
[tex]\[
\begin{array}{l}
y = 2 x - 1 \\
y = x + 1
\end{array}
\][/tex]
is True.
