Question

1) Solve the system by elimination.

{8x−3y=−49

{4x-4y=-32

a) One solution:

b) No solution

c) Infinite number of solutions

2) Solve the system by elimination.

{5x+2y=−5

{3x-5y=28

a) One solution:

b) No solution

c) Infinite number of solutions

Answer 1

1)
8 x - 3 y = -49 ...eqn1
4 x - 4 y = -32 ...eqn2
Multiply eqn2 by 2
8 x - 3 y = -49 ...eqn3
8 x - 8 y = -64 ...eqn4
subtract eqn4 from eqn3
5 y = 15
y = 3
put the value of y in eqn1 to get the x value
8 x - 3 y = -49
8 x - 3 * 3 = -49
8 x = -40
x = -5
So, solutions are:
x = -5
y = 3
Answer: one solution which is
(-5, 3)

2)
5 x + 2 y = -5 ...eqn1
3 x - 5 y = 28 ...eqn2
Multiply eqn1 by 3
Multiply eqn2 by 5
15 x + 6 y = -15 ...eqn3
15 x - 25 y = 140 ...eqn4
subtract eqn4 from eqn3
31 y = -155
y = -5
put the value of y in eqn1 to get the x value
5 x + 2 y = -5
5 x + 2 * -5 = -5
5 x = 5
x = 1
So, solutions are:
x = 1
y = -5
Answer: one solution which is
(1, -5)