To determine whether the point [tex]\((2, -3)\)[/tex] is on the graph of the equation [tex]\(x + y = 1\)[/tex], we need to substitute the coordinates of the point into the equation and verify if the equation holds true.
Let's go through this step-by-step:
1. Substitute the x-coordinate: In the equation [tex]\(x + y = 1\)[/tex], substitute [tex]\(x\)[/tex] with 2.
[tex]\[
2 + y = 1
\][/tex]
2. Substitute the y-coordinate: In the same equation, substitute [tex]\(y\)[/tex] with -3.
[tex]\[
2 + (-3) = 1
\][/tex]
3. Simplify the left-hand side: Perform the arithmetic operation on the left-hand side.
[tex]\[
2 - 3 = -1
\][/tex]
4. Compare to the right-hand side: Check whether the simplified left-hand side is equal to the right-hand side.
[tex]\[
-1 = 1 \quad \text{(This is not true)}
\][/tex]
Since [tex]\(-1\)[/tex] is not equal to [tex]\(1\)[/tex], the equation [tex]\(2 + (-3) = 1\)[/tex] does not hold true.
Therefore, the point [tex]\((2, -3)\)[/tex] is not on the graph of the equation [tex]\(x + y = 1\)[/tex].
