Question

a) determine whether the ordered pair is a solution to the given system of equations.

1. (1, 5) ; $-5m + 6n = 25$; $-7m + 8n = 33$
2. $(-2, 0)$ ; $8x - 3y = -16$; $50 = -9x - 2y$
3. $(7, -4)$ ; $9b + 4a = -8$; $6a + 5b - 42 = 0$
4. $(-3, -2)$ ; $-7c - 4d = 29$; $3c = -7 + d$

Explanation:

1) Ordered pair (1,5)

Step1: Substitute into first equation

$m=1, n=5$: $-5(1)+6(5)=-5+30=25$

Step2: Substitute into second equation

$m=1, n=5$: $-7(1)+8(5)=-7+40=33$

Step3: Verify equality

Both equations equal their right-hand sides.

2) Ordered pair (-2,0)

Step1: Substitute into first equation

$x=-2, y=0$: $8(-2)-3(0)=-16-0=-16$

Step2: Substitute into second equation

$x=-2, y=0$: $-9(-2)-2(0)=18-0=18
eq50$

Step3: Verify equality

Second equation fails.

3) Ordered pair (7,-4)

Step1: Substitute into first equation

$a=7, b=-4$: $9(-4)+4(7)=-36+28=-8$

Step2: Substitute into second equation

$a=7, b=-4$: $6(7)+5(-4)-42=42-20-42=-20
eq0$

Step3: Verify equality

Second equation fails.

4) Ordered pair (-3,-2)

Step1: Substitute into first equation

$c=-3, d=-2$: $-7(-3)-4(-2)=21+8=29$

Step2: Substitute into second equation

$c=-3, d=-2$: $3(-3)=-9$; $-7+(-2)=-9$

Step3: Verify equality

Both equations equal their right-hand sides.

Answer:

1. (1, 5) is a solution to the system.
2. (-2, 0) is not a solution to the system.
3. (7, -4) is not a solution to the system.
4. (-3, -2) is a solution to the system.