Question

In the following exercise, solve the systems of equations by elimination.

$\left\{\begin{array}{l}x-4y=-1\\ -3x+12y=3\end{array}\right.$

Short answer

The system has infinitely many solutions.

Step-by-step solution

Step 1. Given Information 

The given linear equations are :

$$\begin{gathered} x-4y=-1 \\ -3x+12y=3 \end{gathered}$$

Step 2. Calculating the value of y

To calculate the value of $y$, we have to eliminate the $x$term. For which we will do the following changes in the equation, so that $x$term can be easily eliminated.

Multiply the first equation by$3$

$$\begin{gathered} 3\left(x-4y=-1\right) \\ 3x-12y=-3 \end{gathered}$$

now, the equations are

$$\begin{gathered} 3x-12y=-3 \\ -3x+12y=3 \end{gathered}$$

now simply add the equations

$3x-12y=-3-3x+12y=30=0$

this means that the above equation is satisfied for all the values of $y$and $x$.