Question

Drag the tiles to the correct boxes to complete the pairs.

Answer 1

Answer:

One Solution:

$-3x+y=7\\21x+4y=-8$

Infinitely Many Solution:

$31x-y=4\\61x-2y=8$

No Solution:

$y=-4r+5\\y=-4r+1$

Step-by-step explanation:

System 1

$-3x+y=7\\21x+4y=-8$

$Eq(1)\times7+Eq(2)\\11y=41\\y=\frac{41}{11} \\\\From\ Eq\ 1\\-3x+\frac{41}{11} =7\\-3x=7-\frac{41}{11}\\-3x=\frac{36}{11}\\x=\frac{-12}{11}$

Hence only one solution $(-\frac{12}{11},\frac{41}{11})$

System 2

$31x-y=4\\61x-2y=8$

Both represents the same line. Hence these have infinitely many solutions.

System 3

$y=-4r+5\\y=-4r+1$

Compare both the lines with $y=mx+b$, where m is the slope.

$m=-4$ for both the lines.

Hence these two lines are parallel that means there does not exists any point of intersection

So this system will not have any solution.