Review for Mastery
Solving Systems by Elimination continued
A system of equations can be solved by graphing, substitution, or elimination.
Use graphing if both equations are solved for $y$, or if you want an estimate of the solution.
Use substitution if either equation is solved for a variable, or has a variable with a coefficient of 1 or -1.
Use elimination if both equations have the same variable with the same or opposite coefficients.
It may be necessary to manipulate your equations to get them in any of the three forms above.
Solve $\begin{cases} y = 3 - x \\ 2x - y = 6 \end{cases}$
One equation is solved for a variable. Use substitution.
$3 - x$
$2x - y = 6$
$2x - (3 - x) = 6$
$3x - 3 = 6$
$+3 \quad +3$
$3x = 9$
$x = 3$
Substitute $x + 2$ for $y$.
Substitute $x = 3$ into one of the original equations to find the value of $y$.
$y = 3 - x$
$y = 3 - 3$
$y = 0$
The solution is $(3, 0)$.
Solve $\begin{cases} -2x - y = -5 \\ 3x + y = -1 \end{cases}$
$-2x - y = -5$
$3x + y = -1$
$x + 0 = -6$
$x = -6$
The equations have the same variable with opposite coefficients. Use elimination.
Substitute $x = -6$ into one of the original equations to find the value of $y$.
$3x + y = -1$
$3(-6) + y = -1$
$-18 + y = -1$
$+18 \quad +18$
$y = 17$
The solution is $(-6, 17)$.
Solve each system by any method.
5. $\begin{cases} y = x + 3 \\ -2x + y = -4 \end{cases}$
6. $\begin{cases} 4x + y = 10 \\ -2x - y = 4 \end{cases}$
7. $\begin{cases} 2x + y = 8 \\ 3x + 5y = 5 \end{cases}$