Q. 68 - Intermediate Algebra

Question

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

Step-by-Step Solution

Answer

The possible number of solution is one.

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.