Question

How many solutions does the system of equations below have? y = – 2x − 6 y = – 2 x + 3 5 one solution one solution two solutions two solutions infinitely many solutions infinitely many solutions no solution

Answer 1

Answer: No solution

Explanation:

Given

Pair of lines are

`\Rightarrow y=-2x-6\ \text{and}\ y=-2x+35`

For lines
`a_1x+b_1y+c_1=0\ \text{and}\ a_2x+b_2y+c_2=0` will be parallel when

`\Rightarrow (a_1)/(a_2)=(b_1)/(b_2)\\eq(c_1)/(c_2)`

Rewrite the given lines

`y+2x+6=0\ \text{and}\ y+2x-35=0`

`\Rightarrow (2)/(2)=(1)/(1)\\eq(6)/(-35)\\\\\Rightarrow (1)/(1)=(1)/(1)\\eq(6)/(-35)`

Thus, the given lines are parallel. Therefore, there is no solution for the givebn pair of lines.