방정식과 부등식 전체 문제

Solve a System of Equations by Elimination

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

$\left\{\begin{array}{l}3x+8y=67 \\ 5x+3y=60\end{array}\right.$

Solve a System of Equations by Elimination

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

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

Solve a System of Equations by Elimination

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

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

Solve a System of Equations by Elimination

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

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

Solve a System of Equations by Elimination

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

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

Solve a System of Equations by Elimination

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

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

Solve a System of Equations by Elimination

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

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

Solve a System of Equations by Elimination

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

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

Solve a System of Equations by Elimination

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

$\left\{\begin{array}{l}-3x-y=8 \\ 6x+2y=-16\end{array}\right.$

Solve a System of Equations by Elimination

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

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

Choose the Most Convenient Method to Solve a System of Linear Equations

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

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

Choose the Most Convenient Method to Solve a System of Linear Equations

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

ⓐ $\left\{\begin{array}{l}y=7x-5 \\ 3x-2y=16\end{array}\right.$ ⓑ $\left\{\begin{array}{l}12x-5y=-42 \\ 3x+7y=-15\end{array}\right.$

Choose the Most Convenient Method to Solve a System of Linear Equations

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

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

Choose the Most Convenient Method to Solve a System of Linear Equations

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

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

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

Solve the system of equations $\left\{\begin{array}{l}x+y=10 \\ x-y=6\end{array}\right.$

ⓐ by graphing ⓑ by substitution ⓒ Which method do you prefer? Why?

The sum of twice a number and nine is 31. Find the number.

Twins Jon and Ron together earned $96,000 last year. Ron earned $8000 more than three times what Jon earned. How much did each of the twins earn?