Systems of Linear Equations

Determine whether the ordered pair is a solution to the system $\left\{\begin{array}{l}3x+y=0\\ x+2y=-5\end{array}\right.$

1. $(1,-3)$
   
2. $(0,0)$
   

Determine whether the ordered pair is a solution to the system $\left\{\begin{array}{l}x-3y=-8\\ -3x-y=4\end{array}\right.$

1. $(2,-2)$
   
2. $(-2,2)$
   

Solve the system by graphing: $\left\{\begin{array}{l}x-3y=-3\\ x+y=5\end{array}\right.$

Solve the system by graphing: $\left\{\begin{array}{l}-x+y=1\\ 3x+2y=12\end{array}\right.$

Solve the system by graphing: $\left\{\begin{array}{l}-x+y=1\\ 2x+y=10\end{array}\right.$$\left\{\begin{array}{l}-x+y=1\\ 2x+y=10\end{array}\right.$

Solve the system by graphing: $\left\{\begin{array}{l}2x+y=6\\ x+y=1\end{array}\right.$$\left\{\begin{array}{l}2x+y=6\\ x+y=1\end{array}\right.$

Solve the system by graphing: $\left\{\begin{array}{l}y=-\frac{1}{4}x+2\\ x+4y=-8\end{array}\right.$

Solve the system by graphing:  $\left\{\begin{array}{l}y=3x-1\\ 6x-2y=6\end{array}\right.$

Solve the system by graphing: 

$\left\{\begin{array}{l}y=-3x-6\\ 6x+2y=-12\end{array}\right.$

Solve the system by graphing:  $\left\{\begin{array}{l}y=\frac{1}{2}x-4\\ 2x-4y=16\end{array}\right.$

Without graphing, determine the number of solutions and then classify the system of equations. 

$$\begin{gathered} \text{ (a) }\left\{\begin{array}{l}y=-2x-4\\ 4x+2y=9\end{array}\right. \\ \text{ (b) }\left\{\begin{array}{l}3x+2y=2\\ 2x+y=1\end{array}\right. \end{gathered}$$

Without graphing, determine the number of solutions and then classify the system of equations.

$$\begin{gathered} \text{(a) }\left\{\begin{array}{l}y=\frac{1}{3}x-5\\ x-3y=6\end{array}\right. \\ (b) \left\{\begin{array}{l}x+4y=12\\ -x+y=3\end{array}\right. \end{gathered}$$

Solve the system by substitution: $\left\{\begin{array}{l}-2x+y=-11\\ x+3y=9\end{array}\right.$

Solve the system by substitution: $\left\{\begin{array}{l}2x+y=-1\\ 4x+3y=3\end{array}\right.$

Solve the system by substitution: $\left\{\begin{array}{l}x-4y=-4\\ -3x+4y=0\end{array}\right.$

Solve the system by substitution: 

Solve the system by elimination: $\left\{\begin{array}{l}3x+y=5\\ 2x-3y=7\end{array}\right.$

Solve the system by elimination: $\left\{\begin{array}{l}4x+y=-5\\ -2x-2y=-2\end{array}\right.$

Solve the system by elimination: 

Solve the system by elimination: $\left\{\begin{array}{l}7x+8y=4\\ 3x-5y=27\end{array}\right.$

Solve each system by elimination: $\left\{\begin{array}{l}\frac{1}{3}x-\frac{1}{2}y=1\\ \frac{3}{4}x-y=\frac{5}{2}\end{array}\right.$

In the following exercises, solve each system by graphing $\left\{\begin{array}{l}x-2y<3\\ y\le 1\end{array}\right.$

Solve the system by elimination $\left\{\begin{array}{l}x+2y=6\\ y=-\frac{1}{2}x+3\end{array}\right.$

Solve each system by elimination: $\left\{\begin{array}{l}x+\frac{3}{5}y=-\frac{1}{5}\\ -\frac{1}{2}x-\frac{2}{3}y=\frac{5}{6}\end{array}\right.$

Solve the system by elimination$\left\{\begin{array}{l}5x-3y=15\\ y=-5+\frac{5}{3}x\end{array}\right.$

In the following exercise, solve each system of equations using a matrix.

$\left\{\begin{array}{l}2x-y+3z=-3\\ -x+2y-z=10\\ x+y+z=5\end{array}\right.$

For each system of linear equations decide whether it would be more convenient to solve it by substitution or elimination. Explain your answer.

$\left\{\begin{array}{l}4x-5y=-32\\ 3x+2y=-1\end{array}\right.$

$\left\{\begin{array}{l}6x-2y=12\\ 3x+7y=-13\end{array}\right.$

For each system of linear equations decide whether it would be more convenient to solve it by substitution or elimination. Explain your answer. 

$$\begin{gathered} \left\{\begin{array}{l}4x-5y=-32\\ 3x+2y=-1\end{array}\right. \\ \left\{\begin{array}{l}x=2y-1\\ 3x-5y=-7\end{array}\right. \end{gathered}$$

In the following exercises, determine if the following points are solutions to the given system of equations.

$\left\{\begin{array}{l}2x-6y=0\\ 3x-4y=5\end{array}\right.$

In the following exercises, determine if the following points are solutions to the given system of equations. 

$\left\{\begin{array}{l}-3x+y=8\\ -x+2y=-9\end{array}\right.$

$\begin{array}{l}\left(\mathrm{a}\right)\left(-5,-7\right)\\ \left(\mathrm{b}\right)\left(-5,7\right)\end{array}$

In the following exercises, determine if the following points are solutions to the given system of equations.

$\left\{\begin{array}{l}x+y=2\\ y=\frac{3}{4}x\end{array}\right.$

$$\begin{gathered} \left(\mathrm{a}\right) \left(\frac{8}{7},\frac{6}{7}\right) \\ \left(\mathrm{b}\right) \left(1,\frac{3}{4}\right) \end{gathered}$$

In the following exercises, determine if the following points are solutions to the given system of equations.

$\left\{\begin{array}{l}2x+3y=6\\ y=\frac{2}{3}x+2\end{array}\right.$

a.$(-6,2)$

b.$(-3,4)$

In the following exercises, Solve the system of equation by graphing 

$$\begin{gathered} 3x+y=-3 \\ 2x+3y=5 \end{gathered}$$

In the following exercises, solve the following systems of equations by graphing.

$$\begin{gathered} -x+y=2 \\ 2x+y=-4 \end{gathered}$$

In the following exercises, solve the following systems of equations by graphing.  

$$\begin{gathered} y=x+2 \\ y=-2x+2 \end{gathered}$$

In the following exercises, solve the following systems of equations by graphing

In the following exercises, solve the following systems of equations by graphing. 

$$\begin{gathered} y=x-2 \\ y=-3x+2 \end{gathered}$$

In the following exercises, solve the following systems of equations by graphing. 

$$\begin{gathered} y=\frac{3}{2} x+1 \\ y=-\frac{1}{2}x+5 \end{gathered}$$

In the following exercises, solve the following systems of equations by graphing.  

$$\begin{gathered} y=\frac{2}{3} x-2 \\ y=-\frac{1}{3} x-5 \end{gathered}$$

In the following exercises, solve the following systems of equations by graphing.  

$$\begin{gathered} x+y=-4 \\ -x+2y=-2 \end{gathered}$$

In the following exercises, solve the following systems of equations by graphing. 

$$\begin{gathered} -x+3y=3 \\ x+3y=3 \end{gathered}$$

In the following exercises, solve the following systems of equations by graphing. 

In the following exercises, solve the following systems of equations by graphing.

$$\begin{gathered} 2x-y=4 \\ 2x+3y=12 \end{gathered}$$

In the following exercises, solve the following system of equations by graphing.

$\left\{\begin{array}{l}x+3y=-6\\ y=-\frac{4}{3}x+4\end{array}\right.$

In the following exercises,solve the following system of equations by graphing.

$\left\{\begin{array}{l}-x+2y=-6\\ y=-\frac{1}{2}x-1\end{array}\right.$

In the following exercises, solve the following system of equations by graphing.

$\left\{\begin{array}{l}-2x+4y=4\\ y=\frac{1}{2}x\end{array}\right.$

In the following exercises, solve the following system of equations by graphing.

$\left\{\begin{array}{l}3x+5y=10\\ y=-\frac{3}{5}x+1\end{array}\right.$

In the following exercises, solve the following system of equations by graphing.

$\left\{\begin{array}{l}4x-3y=8\\ 8x-6y=14\end{array}\right.$

In the following exercises, solve the following system of equations by graphing.

$\left\{\begin{array}{l}x+3y=4\\ -2x-6y=3\end{array}\right.$

In the following exercises, solve the system of linear equations by graphing.

 $\left\{\begin{array}{l}x=-3y+4\\ 2x+6y=8\end{array}\right.$