Question

Please help!

Match each system on the left with the number of solutions that it has on the right.

Answer 1

1. No solution

2. Infinitely many solutions

3. Infinitely many solutions

4. One solution

Explanation:

1.

x=y-3

2x-2y=6

Substitute x=y-3 in (2)

2(y-3)-2y=6

2y-6-2y=6

2y-2y=6+6

0=12

No solution

2.

5x+2y=-7

10x+4y=-14

Multiply (1) by 2 and (2) by 1

10x+4y=-14

10x+4y=-14

Subtract (3) from (4)

0+0=0

0=0

Infinitely many solutions

3.

y=2x+1

4x-2y=-2

Substitute y=2x+1 into (2)

4x-2(2x+1)=-2

4x-4x-2=-2

4x-4x=-2+2

0=0

Infinitely many solutions

4.

9x+6y=15

2y= -1+3x

From 2

2y+1-3x=0

-3x+2y=-1

9x+6y=15 (1)

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

Multiply (2) by 3

-9x+6y=-3

9x+6y=15

Subtract (3) from (1)

9x-(-9x)=15-(-3)

9x+9x=15+3

18x=18

x=18/18

=1

x=1

Substitute x=1 into (1)

9x+6y=15

9(1)+6y=15

9+6y=15

6y=15-9

6y=6

y=6/6

=1

One solution