Respuesta :

Answer:

1-c

2-b

3-a

Step-by-step explanation:

1. 7y=14

y=2

-7y=-14

y=2

so the equation has one solution

2. 0=0

so the equation has infinite solution

3. 0=2 false

so the equation has no solution

1 solution

8x+7y=30

8x-7y=2

infinitely many solutions

-8x+7y=-2

8x-7y=2

no  solution

8x-7y=2

-8x+7y=2

Explanation

The number of solutions of a pair of linear equations are determined by the following criteria

1 solution

-[tex]a1/a2 \neq b1/b2[/tex]

in the first pair [tex]a1/a2=8/8=1[/tex]

[tex]b1/b2=7/-7=-1[/tex]

therefore [tex]a1/a2 \neq b1/b2[/tex]

infinitely many solution

[tex]a1/a2=b1/b2=c1/c2[/tex]

In the second pair of equations -8x+7y+2=0 and 8x-7y-2=0

[tex]a1/a2=-8/8=-1\\b1/b2=7/-7=-1\\c1/c2=2/-2=-1[/tex]

since [tex]a1/a2=b1/b2=c1/c2[/tex], the pair of equations have infinitely many solutions

no solution

[tex]a1/a2=b1/b2\neq c1/c2[/tex]

in the third pair of equation

[tex]a1/a2=8/-8=-1\\b1/b2=-7/7=-1\\c1/c2=-2/-2=1[/tex]

Here [tex]a1/a2=b1/b2\neq c1/c2[/tex]

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