Question

How many solutions does the system have?

5x - y = 2
5x - y = -2

Choose 1 answer:

A. Exactly one solution
B. No solutions
C. Infinitely many​

Answer 1

B. No solution

Step-by-step explanation:

5x - y = 2

5x - y = -2

If we will convert into standard form (ax + by + c = 0)

5x - y = 2

=> 5x - y - 2 = 0...(i)

5x - y = - 2

=> 5x - y + 2 = 0...(ii)

Now,

$a_{1} = 5 \: . \: b_{1} = - 1 \: . \: c_{1} = - 2 \\ a_{2} = 5 \: . \: b_{2} = - 1 \: . \: c_{2} = 2$

So,

$\frac{a _{1}}{a_{2}} = \frac{5}{5} = 1 \\ \\ \frac{b_{1}}{b_{2}} = \frac{ - 1}{ - 1} = 1 \\ \\ \frac{c_{1}}{c_{2}} = \frac{ - 2}{2} = - 1$

So,

$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}}≠ \frac{c_{1}}{c_{2}}$

So, there will be no solution, if we draw it on graph the lines will be parallel.

hope it helps.

Answer 2

Ⓑ. No Sollutions... ↥↥↥