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

Step-by-step 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

$\Rightarrow \dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq\dfrac{c_1}{c_2}$

Rewrite the given lines

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

$\Rightarrow \dfrac{2}{2}=\dfrac{1}{1}\neq\dfrac{6}{-35}\\\\\Rightarrow \dfrac{1}{1}=\dfrac{1}{1}\neq\dfrac{6}{-35}$

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