Question

Substitution Method

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

$\left\{\begin{array}{l}3x+y=1\\ 5x+2y=1\end{array}\right.$

Short answer

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

Step-by-step solution

Step 1. Given information

We are given the system of linear equations that is-

$\left\{\begin{array}{l}3x+y=1\\ 5x+2y=1\end{array}\right.$

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 process of the system of equations, we will calculate the result.

Step 3. Calculation

We substitute the values

$\begin{array}{l}5x+2(1-3x)=1\\ 5x+2-6x=1\\ 2-x=1\\ x=1\end{array}$

Then we calculate the value of $y$

$\begin{array}{l}y=1-3x\\ y=1-3\left(1\right)\\ y=1-3\\ y=-2\end{array}$

The solution of the system is then

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