Question

$x+2y=5$
$y=3x-8$
a there is no solution.
b there are infinitely many solutions.
c there is exactly one solution at (5, -8).
d there is exactly one solution at (3, 1).

Explanation:

Step1: Substitute $y=3x-8$ into first equation

$x + 2(3x - 8) = 5$

Step2: Expand and simplify the equation

$x + 6x - 16 = 5$
$7x - 16 = 5$

Step3: Solve for $x$

$7x = 5 + 16$
$7x = 21$
$x = \frac{21}{7} = 3$

Step4: Substitute $x=3$ into $y=3x-8$

$y = 3(3) - 8 = 9 - 8 = 1$

Answer:

D. There is exactly one solution at (3, 1).