Question

Tell whether the System has one solution infinite solution many solutions or no solutions 5x-3y=10 10x+6y=20

Answer 1

One solution

Explanation:

We are given the following system of equations and we are to tell if the system has one solution, infinite solution, many solutions or no solutions:

`5x-3y=10` --- (1)

`10x+6y=20` --- (2)

If we take the common out from (2), we get:

`2(5x+3y) = 20`

`5x+3y = 10` --- (3)

So adding the two equations (1) and (3) gives 10x=20 ⇒ x=2.

Therefore, this system of equations has one solution.

Answer 2

The system has one solution.

EXPLANATION

The given system is

1st: 5x-3y=10

2nd: 10x+6y=20

Make y the subject in the first equation to get:

`y = (5)/(3) x + (10)/(3)`

Solve for y in the second equationquation to get;

`y = - (5)/(3) x + (10)/(3)`

The slope of the two equations are not the same.

The two lines will intersect at exactly one point.

.The system has one solution.