Answer
A system of linear equations can be solved using the addition method. This involves isolating a variable and solving an equation consisting of only one variable.
Work Step by Step
A system of linear equations can be solved using the addition method. This involves isolating a variable and solving an equation consisting of only one variable.
This is done by using addition of two equations to eliminate a variable.
For example, consider the system
\[\begin{align}
& 3x+5y=-2 \\
& 2x+3y=0 \\
\end{align}\]
Now, \[x\] coefficient of both the equations is made same by multiplying the first equation with \[2\] and the second equation by \[-3\]. The equations are then added as follows:
\[\begin{align}
& \text{ }6x+10y=-4 \\
& \underline{-6x-9y=0\text{ }} \\
& \text{ }y=-4 \\
\end{align}\]
Substitute this value in any of the equation to find the value of \[x\]
\[\begin{align}
& 2x+3(-4)=0 \\
& x=6
\end{align}\]
Thus, the solution of the system of equations is ordered pair \[\left( 6,-4 \right)\].
