Question

1) Solve by Substitution.

{x+2y=−1

{-6y=3+3x

a) One solution:   

b) No solution

c) Infinite number of solutions

2) Solve by Substitution

{4x+y=−15

{2y=-27-8x

a) One solution:

b) No solution

c) Infinite number of solutions

3) Solve the system by elimination.

{−x−2y=4

{2x+2y=-8

a) One solution:

b) No solution

c) Infinite number of solutions

Answer 1

1)

x+2y=−1 , so x = -2y -1

Substitute -2y -1 for x in -6y=3+3x

-6y=3+3(-2y-1)

-6y= 3 -6y -3

-6y= -6y

Since both sides are same, equation has ininite solution.

c) Infinite number of solutions

2)

4x+y=−15 so y= -4x -15

Substitute -4x-15 for y in 2y=-27-8x

2(-4x-15 )=-27-8x

-8x -30 = -8x -27

-30= -27

Since this is a false statement, equation has No solution.

b) No solution

3)

−x−2y=4

2x+2y=-8

Multiply first equation by 2

-2x -4y= 8

2x +2y= -8

Add both

6y =0

y =0/6

y=0

hence

2x+2(0)=-8

2x = -8

x= -4

So,

x = -4, y = 0

a) One solution: