Solve the system of linear equation by substitution method.
$y = 2 x + 5 y = 3 x - 1$

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Solution

Find the solution to the system of linear equations using the substitution method.
The given system of equations are $y = 2 x + 5 and y = 3 x - 1$ .
In the substitution method, the value of any one variable is substituted from one equation to another, and solve the obtained equation for a variable. Then put the solution in any of the equations to find the solution for the second variable.
Substitute $y = 2 x + 5$ in $y = 3 x - 1$ and solve the equation:
$\begin{array}{rcl} y & = & 3 x - 1 \\ \Rightarrow & 2 x + 5 = 3 x - 1 \\ \Rightarrow & 2 x - 3 x = - 5 - 1 \\ \Rightarrow & - x = - 6 x \\ \Rightarrow & x = 6 \end{array}$
Substituting $x = 6$ in the given equations $y = 3 x - 1$ to find the value of $y$ :
$\begin{array}{rcl} y & = & 3 x - 1 \\ \Rightarrow & y = 3 (6) - 1 \\ \Rightarrow & y = 18 - 1 \\ \Rightarrow & y = 17 \end{array}$
Hence, the solution of the system of linear equation is $x = 6$ and $x = 17$ .

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