Question

How many solutions does the following system have ? 2x+3y=1 and -3x-2y=-1

Answer 1

you can use one solution

Answer 2

The given system of equation have one solution.

Explanation:

The given system of equations is

`2x+3y=1`

`-3x-2y=-1`

A system of equation has two equation
`a_1x+b_1y=c_1` and
`a_2x+b_2y=c_2`.

1. If
`(a_1)/(a_2)=(b_1)/(b_2)\\eq (c_1)/(c_2)`, then system of equations has no solution.

2. If
`(a_1)/(a_2)=(b_1)/(b_2)=(c_1)/(c_2)`, then system of equations has infinite solution.

3. If
`(a_1)/(a_2)neq (b_1)/(b_2)`, then system of equation has one solution.

In the given system of equation,

`a_1=2,b_1=3,c_1=1,a_2=-3,b_2=-2, c_2=-1`

`(a_1)/(a_2)=(2)/(-3)=-(2)/(3)`

`(b_1)/(b_2)=(3)/(-2)=-(3)/(2)`

Since
`(a_1)/(a_2)neq (b_1)/(b_2)`, therefore the given system of equation have one solution.