To determine the solution of the system of equations given by
[tex]\[ y = 2x - 5 \][/tex]
and
[tex]\[ y = x + 3 \][/tex]
we need to find the point at which these two lines intersect.
The point of intersection is the set of coordinates [tex]\((x, y)\)[/tex] that satisfies both equations simultaneously.
Start by setting the two equations equal to each other, since both equations equal [tex]\(y\)[/tex]:
[tex]\[ 2x - 5 = x + 3 \][/tex]
To solve for [tex]\(x\)[/tex], first isolate [tex]\(x\)[/tex] on one side of the equation:
[tex]\[ 2x - x = 3 + 5 \][/tex]
Simplify the equation:
[tex]\[ x = 8 \][/tex]
Now, substitute [tex]\(x = 8\)[/tex] back into either of the original equations to find [tex]\(y\)[/tex]. We'll use the second equation for this purpose:
[tex]\[ y = 8 + 3 \][/tex]
So,
[tex]\[ y = 11 \][/tex]
Therefore, the solution to this system of equations is the point where the two lines intersect:
[tex]\[ (x, y) = (8, 11) \][/tex]
So, the correct answer is:
C. [tex]\((8, 11)\)[/tex]
