Question

What is the solution to the system of linear equations below? 2/5x−y=6 −2x+5y=−30 Select one: A. (-13, 14) B. (-5, -8) C. no solution D. infinitely many solutions

Answer 1

Answer:

D. Infinitely many solutions

Step-by-step explanation:

$-\frac{2}{5}x-y=6 | -2x+5y=-30$

1.Since neither equation contains an isolated. However, we can isolate -y in the first equation by adding $\frac{2}{5}x$ to both sides.

Like this: $\frac{2}{5}x-\frac{2}{5}x-y=6-\frac{2}{5}x$

ending up with $y=6-\frac{2}{5}x$

2.Now, we can change y to a positive y. By doing so, we divide -y by the entire equation.

Like this $\frac{-y=6-\frac{2}{5}x }{-y}$

Ending with $y=-6+\frac{2}{5}x$

3.Now, we can plug the expression $-6+\frac{2}{5}x$ into the second equation as a substitute for y, and solve for x. Then, we can use x to calculate y.

Like this $-2x+5(-6+\frac{2}{5}x)=-30\\ -2x-30+2x=-30$

4. Since -2x+2x would cancel out and leave -30=-30. This is true because we know -30 equals -30 with no variable in sight.