Question

Hi! I would like some help on these questions please?

Solve the system of equations using the linear combination method.

{5p - 3q= -39
-2p - 3q = 3

Solve the system of equations using the linear combination method.

{4x - 3y = 12
7x - 3y = 3

Thank you!

Answer 1

first one
eliminate q's
multiply 2nd equation by -1 and add to 2nd

5p-3q=-39
2p+3q=-3 +
7p+0q=-42

7p=-42
divide both sides by 7
p=-6
sub back

-2p-3q=3
-2(-6)-3q=3
12-3q=3
minus 12
-3q=-9
divide -3
q=3

p=-6
q=3







2nd one

eliminate y's
multiply first equation by -1 and add to 2nd

-4x+3y=-12
7x-3y=3 +
3x+0y=-9

3x=-9
divide both sides by 3
x=-3
sub back
4x-3y=12
4(-3)-3y=12
-12-3y=12
-3y=24
y=-8

(x,y)
(3,-8)

Answer 2

Below I attached the working out for both set of systems.

For the first, solution to the system is p = -6 ; q = 3
For the second, the solution to the system is x = -3 ; y = -8