SOLUTION: which of the following system of linear equation has an infinite number of solutions? please show work. a. 2x+5y=1, 6x+15y=3 b. x+y=10, x-y=4 c. x+y=10, x-y=16 d. x-2y=8, 2x+7

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: which of the following system of linear equation has an infinite number of solutions? please show work. a. 2x+5y=1, 6x+15y=3 b. x+y=10, x-y=4 c. x+y=10, x-y=16 d. x-2y=8, 2x+7      Log On


   

Question 969604: which of the following system of linear equation has an infinite number of solutions? please show work.
a. 2x+5y=1, 6x+15y=3
b. x+y=10, x-y=4
c. x+y=10, x-y=16
d. x-2y=8, 2x+7y=-16
Answer by erica65404(394) About Me  (Show Source):
You can put this solution on YOUR website!
Two equations will have an infinite amount of solutions if they are identical to one another.
To find out if they are identical, solve for y.

a) Solve each equation for y...
2x%2B5y=1
5y=-2x%2B1
y=%28-2x%29%2F5+%2B+1%2F5

6x%2B15y=3
15y=-6x%2B3
y=%28-6x%29%2F15%2B+3%2F15
simplify
y=%28-2x%29%2F5+%2B+1%2F5

These equations are identical so they have an infinite amount of solutions.
The answer is A.
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