Systems of Linear Equations

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

$\left\{\begin{array}{l}4x=3y+7\\ 8x-6y=14\end{array}\right.$

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

$\left\{\begin{array}{l}2x+y=6\\ -8x-4y=-24\end{array}\right.$

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

$\left\{\begin{array}{l}5x+2y=7\\ -10x-4y=-14\end{array}\right.$

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

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

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

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

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

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

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

$$\begin{gathered} y=-\frac{1}{2}x+5 \\ x+2y=10 \end{gathered}$$

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

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

Solve the systems of equations by substitution.

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

Solve the systems of equations by substitution. 

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

Solve the systems of equations by substitution. 

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

Solve the systems of equations by substitution. 

$\left\{\begin{array}{l}x-3y=-9\\ 2x+5y=4\end{array}\right.$

Solve the systems of equations by substitution.

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

Solve the system of equations by substitution

$\left\{\begin{array}{l}-2x+2y=6\\ y=-3x+1\end{array}\right.$

Solve the system of equations by substitution

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

Solve the system of equations by substitution

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

Solve the system of equations by substitution

$\left\{\begin{array}{l}2x+y=5\\ x-2y=-15\end{array}\right.$

Solve the system of equations by substitution

$\left\{\begin{array}{l}4x+y=10\\ x-2y=-20\end{array}\right.$

Solve the system of equations by substitution

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

Solve the system of equations by substitution

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

Solve the system of equations by substitution

$\left\{\begin{array}{l}x=2y\\ 4x-8y=0\end{array}\right.$

Solve the system of equations by substitution

$\left\{\begin{array}{l}2x-16y=8\\ -x-8y=-4\end{array}\right.$

Solve the system of equations by substitution

$\left\{\begin{array}{l}y=\frac{7}{8}x+4\\ -7x+8y=6\end{array}\right.$

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

$$\begin{gathered} y=-\frac{2}{3}x+5 \\ 2x+3y=11 \end{gathered}$$

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

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

$$\begin{gathered} 6x-5y=-1 \\ 2x+y=13 \end{gathered}$$

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

$$\begin{gathered} 2x-5y=7 \\ 3x-y=17 \end{gathered}$$

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

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

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

$$\begin{gathered} 3x-5y=-9 \\ 5x+2y=16 \end{gathered}$$

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

$$\begin{gathered} 4x-3y=3 \\ 2x+5y=-31 \end{gathered}$$

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

$$\begin{gathered} 3x+8y=-3 \\ 2x+5y=-3 \end{gathered}$$

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

$$\begin{gathered} 11x+9y=-5 \\ 7x+5y=-1 \end{gathered}$$

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

$$\begin{gathered} 3x+8y=67 \\ 5x+3y=60 \end{gathered}$$

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

$\left\{\begin{array}{l}2x+9y=-4\\ 3x+13y=-7\end{array}\right.$

In the following exercise, solve the systems of equations by elimination.

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

In the following exercise, solve the systems of equations by elimination.

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

In the following exercise, solve the systems of equations by elimination.

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

In the following exercise, solve the systems of equations by elimination.

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

In the following exercise, solve the systems of equations by elimination.

$\left\{\begin{array}{l}2x+y=3\\ 6x+3y=9\end{array}\right.$

In the following exercise, solve the systems of equations by elimination.

$\left\{\begin{array}{l}x-4y=-1\\ -3x+12y=3\end{array}\right.$

In the following exercise, solve the systems of equations by elimination.

$\left\{\begin{array}{l}x-4y=-1\\ -3x+12y=3\end{array}\right.$

In the following exercise, solve the systems of equations by elimination.

$\left\{\begin{array}{l}4x+3y=2\\ 20x+15y=10\end{array}\right.$

In the following exercises, decide whether it would be more convenient to solve the system of equations by substitution or elimination.

$$\begin{gathered} ⓐ\left\{\begin{array}{l}8x-15y=-32\\ 6x+3y=-5\end{array}\right. \\ ⓑ\left\{\begin{array}{l}x=4y-3\\ 4x-2y=-6\end{array}\right. \end{gathered}$$

$\begin{array}{l}To decide whether it would be more convenient to solve the system of equations by substitution or elimination.\\ \left(a\right) \left\{\begin{array}{l}y=7x-5\\ 3x-2y=16\end{array}\right.\\ \left(b\right)\left\{\begin{array}{l}12x-5y=-42\\ 3x+7y=-15\end{array}\right.\end{array}$

To decide whether it would be more convenient to solve the system of equations by substitution or elimination.

 $$\begin{gathered} \left(a\right) \left\{\begin{array}{l}y=4x+9\\ 5x-2y=-21\end{array}\right. \\ \left(b\right) \left\{\begin{array}{l}9x-4y=24\\ 3x+5y=-14\end{array}\right. \end{gathered}$$

To decide whether it would be more convenient to solve the system of equations by substitution or

elimination.

$$\begin{gathered} \left(a\right)\left\{\begin{array}{l}14x-15y=-30 \\ 7x+2y =10\end{array}\right. \\ \left(b\right)\left\{\begin{array}{l}x=9y-11\\ 2x-7y=-27\end{array}\right. \end{gathered}$$

In a system of linear equations, the two equations have the same intercepts. Describe the possible solutions to the system.

Solve the system of equations by substitution and explain all your steps in words:

$\left\{\begin{array}{l}3x+y=12\\ x=y-8\end{array}\right.$

Solve the system of equations by elimination and explain all your steps in words:

$\left\{\begin{array}{l}5x+4y=10\\ 2x=3y+27\end{array}\right.$

1. Solve the system of equations $\left\{\begin{array}{l}x+y=10\\ x-y=6\end{array}\right.$(a) by graphing (b) by substitution (c) Which method do you prefer? Why?