Question

determine which of the ordered pairs are solutions to the given system of equations.
system: \\( \

$$\begin{cases} 12x + 3y = 15 \\\\ 2x - 3y = 8 \\end{cases}$$

\\), ordered pairs: \\( (0,5), (4,0) \\).
select one:
\\( \circ \\) a. only pair \\( (4,0) \\) is the solution.
\\( \circ \\) b. both pairs are the solution.
\\( \circ \\) c. neither pair is the solution.
\\( \circ \\) d. only pair \\( (0,5) \\) is the solution.

Explanation:

Step1: Test pair (0,5) in Eq1

Substitute $x=0, y=5$ into $12x+3y=15$:
$12(0)+3(5)=0+15=15$, which matches.

Step2: Test pair (0,5) in Eq2

Substitute $x=0, y=5$ into $2x-3y=8$:
$2(0)-3(5)=0-15=-15
eq 8$, so not a solution.

Step3: Test pair (4,0) in Eq1

Substitute $x=4, y=0$ into $12x+3y=15$:
$12(4)+3(0)=48+0=48
eq 15$, so not a solution.

Step4: Test pair (4,0) in Eq2

Substitute $x=4, y=0$ into $2x-3y=8$:
$2(4)-3(0)=8-0=8$, which matches.

Answer:

C. Neither pair is the solution.