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

Answer:

The given system of equation have one solution.

Step-by-step 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 $\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq \frac{c_1}{c_2}$, then system of equations has no solution.

2. If $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$, then system of equations has infinite solution.

3. If $\frac{a_1}{a_2}neq \frac{b_1}{b_2}$, then system of equation has one solution.

In the given system of equation,

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

$\frac{a_1}{a_2}=\frac{2}{-3}=-\frac{2}{3}$

$\frac{b_1}{b_2}=\frac{3}{-2}=-\frac{3}{2}$

Since $\frac{a_1}{a_2}neq \frac{b_1}{b_2}$, therefore the given system of equation have one solution.