Question

Elimination Method

Use the elimination method to find all solutions of the system of equations.

$\left\{\begin{array}{l}3x+4y=10\\ x-4y=-2\end{array}\right.$

Short answer

Hence, all solutions of the system of equations are $x=2\&y=1$

Step-by-step solution

Step 1. Given information

We are given the system of linear equations that is-

$\left\{\begin{array}{l}3x+4y=10\\ x-4y=-2\end{array}\right.$

Step 2. Concept used

The system of linear equations is the collection of one or more linear equations involving the same set of variables.

We need to find all solutions to the system of equations.

By the Elimination Method, we will calculate the result.

Step 3. Calculation

Since the coefficients for the y terms are opposites, we can add the two equations together to eliminate the y terms and then solve for x

$\begin{array}{r}3x+4y=10\\ x-4y=-2\end{array}$

We subtract both equations,

$\begin{array}{l}4x=8\\ x=2\end{array}$

We substitute the values and then solve for y

$\begin{array}{l}2-4y=-2\\ -4y=-4\\ y=1\end{array}$

The solution of the system is then

$(x,y)=(2,1)$