Question

for each ordered pair, determine whether it is a solution to the system of equations.$\begin{cases}7x - 3y = 1 \\-4x + 5y = 6end{cases}$(a) is $(-9, -6)$ a solution?$circ$ yes $circ$ no(b) is $(0, -8)$ a solution?$circ$ yes $circ$ no(c) is $(1, 2)$ a solution?$circ$ yes $circ$ no(d) is $(-2, -5)$ a solution?$circ$ yes $circ$ no

Explanation:

Step1: Test (-9, -6) in Eq1

Substitute $x=-9, y=-6$ into $7x-3y=1$:
$7(-9)-3(-6)=-63+18=-45
eq 1$

Step2: Test (-9, -6) conclusion

Since it fails Eq1, it is not a solution.

Step3: Test (0, -8) in Eq1

Substitute $x=0, y=-8$ into $7x-3y=1$:
$7(0)-3(-8)=0+24=24
eq 1$

Step4: Test (0, -8) conclusion

Since it fails Eq1, it is not a solution.

Step5: Test (1, 2) in Eq1

Substitute $x=1, y=2$ into $7x-3y=1$:
$7(1)-3(2)=7-6=1 = 1$

Step6: Test (1, 2) in Eq2

Substitute $x=1, y=2$ into $-4x+5y=6$:
$-4(1)+5(2)=-4+10=6 = 6$

Step7: Test (1, 2) conclusion

Since it satisfies both equations, it is a solution.

Step8: Test (-2, -5) in Eq1

Substitute $x=-2, y=-5$ into $7x-3y=1$:
$7(-2)-3(-5)=-14+15=1 = 1$

Step9: Test (-2, -5) in Eq2

Substitute $x=-2, y=-5$ into $-4x+5y=6$:
$-4(-2)+5(-5)=8-25=-17
eq 6$

Step10: Test (-2, -5) conclusion

Since it fails Eq2, it is not a solution.

Answer:

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