Question

show that the point (2, 1) is not a solution to the system.
$y = 3x - 5$
$2x + 5y = 7$
the point (2, 1) is not a solution because...

Explanation:

Step1: Substitute into first equation

Substitute $x=2$, $y=1$ into $y=3x-5$:
$1 = 3(2) - 5$
$1 = 6 - 5$
$1 = 1$ (True)

Step2: Substitute into second equation

Substitute $x=2$, $y=1$ into $2x+5y=7$:
$2(2) + 5(1) = 7$
$4 + 5 = 7$
$9 = 7$ (False)

Answer:

the point (2, 1) fails to satisfy the second equation $2x + 5y = 7$ (substitution gives $9=7$, which is false), so it is not a solution to the system.