Question

In a system of linear equations, the two equations have the same intercepts. Describe the possible solutions to the system.

Short answer

The possible number of solution is one.

Step-by-step solution

Step 1. Given information and Assuming Equation

We have been given that the system of linear equations have the same intercepts. So write equation in such a way that $y$intercept of both the equation is same.

Consider equation:

$\left\{\begin{array}{l}3x+y=-3\\ 2x+3y=-9\end{array}\right.$

Step 2. Solving the equation

Solving the two Equation using Elimination method.

$\left\{\begin{array}{l}3x+y=-3\\ 2x+3y=-9\end{array}\right.$

Multiply equation $1$by $3$

$\left\{\begin{array}{l}9x+3y=-9\\ 2x+3y=-9\end{array}\right.$

Substracting both equation we get:

$7x+0y=0$

$x=0$

Now lets substitute $x=0$in equation $2$

$2\left(0\right)+3y=-9$

On solving we get:

$y=-3$

So the solution of the equation is:$(0,-3)$

So there exists only one solution.