Question

for each ordered pair, determine whether it is a solution to the system of equations.
\

$$\begin{cases}2x + 5y = -6 \\\\ 3x - 2y = -9\\end{cases}$$

(a) is (7, -4) a solution?
\bigcirc yes \bigcirc no
(b) is (-5, -3) a solution?
\bigcirc yes \bigcirc no
(c) is (0, 8) a solution?
\bigcirc yes \bigcirc no
(d) is (6, 2) a solution?
\bigcirc yes \bigcirc no

Explanation:

Step1: Test (7, -4) in Eq1

Substitute $x=7, y=-4$ into $2x+5y=-6$:
$2(7)+5(-4)=14-20=-6$, which matches.

Step2: Test (7, -4) in Eq2

Substitute $x=7, y=-4$ into $3x-2y=-9$:
$3(7)-2(-4)=21+8=29
eq-9$, does not match.

Step3: Test (-5, -3) in Eq1

Substitute $x=-5, y=-3$ into $2x+5y=-6$:
$2(-5)+5(-3)=-10-15=-25
eq-6$, does not match.

Step4: Test (0, 8) in Eq1

Substitute $x=0, y=8$ into $2x+5y=-6$:
$2(0)+5(8)=0+40=40
eq-6$, does not match.

Step5: Test (6, 2) in Eq1

Substitute $x=6, y=2$ into $2x+5y=-6$:
$2(6)+5(2)=12+10=22
eq-6$, does not match.

Answer:

(a) No
(b) No
(c) No
(d) No