Answer:
D. Infinitely many solutions
Step-by-step explanation:
[tex]-\frac{2}{5}x-y=6 | -2x+5y=-30[/tex]
1.Since neither equation contains an isolated. However, we can isolate -y in the first equation by adding [tex]\frac{2}{5}x[/tex] to both sides.
Like this: [tex]\frac{2}{5}x-\frac{2}{5}x-y=6-\frac{2}{5}x[/tex]
ending up with [tex]y=6-\frac{2}{5}x[/tex]
2.Now, we can change y to a positive y. By doing so, we divide -y by the entire equation.
Like this [tex]\frac{-y=6-\frac{2}{5}x }{-y}[/tex]
Ending with [tex]y=-6+\frac{2}{5}x[/tex]
3.Now, we can plug the expression [tex]-6+\frac{2}{5}x[/tex] into the second equation as a substitute for y, and solve for x. Then, we can use x to calculate y.
Like this [tex]-2x+5(-6+\frac{2}{5}x)=-30\\ -2x-30+2x=-30\\[/tex]
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.
