Is [tex]\((2,3)\)[/tex] a solution to the following system of linear equations?

[tex]\[
\begin{array}{l}
y = 2x - 1 \\
y = x + 1
\end{array}
\][/tex]

A. True
B. False



Answer :

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.