Answer
A system of linear equations can be solved using the substitution method. This method involves solving either of one equation for one variable in terms of another variable.
Work Step by Step
A system of linear equations can be solved using the substitution method. This method involves solving either of one equation for one variable in terms of another variable.
This expression is then substituted into the other equation that results in the equation in one variable. This equation is then solved for one variable which is then back substituted in the first equation to give the value for another variable. This can be shown for given system of equation as follows:
First, expression for \[y\]in the first equation is substituted in the second equation to convert it into equation with one variable
\[\begin{align}
& 3x+4(3-3x)=6 \\
& 3x-12x+12=6 \\
& 9x=6 \\
& x=\frac{2}{3}
\end{align}\]
This is substituted back in the first equation to solve for \[y\]
\[\begin{align}
& y=3-3\left( \frac{2}{3} \right) \\
& y=3-2 \\
& y=1 \\
\end{align}\]
Thus, the solution of the system of equations is ordered pair \[\left( \frac{2}{3},1 \right)\].
