Exam 11: Systems of Equations

Fill in the blank with one of the words or phrases listed below. system of linear equations solution consistent independent dependent inconsistent substitution addition -Two algebraic methods for solving systems of equations are_____________ and_____________ .

Decide whether or not the ordered pair satisfies the system of linear equations. -(-9, -5); $\left\{ \begin{array} { l } 2 x = - 22 - y \\x + 4 y = - 29\end{array} \right.$

Solve the system of equations by the addition method. - $\left\{ \begin{array} { l } 4 x - 4 y = 10 \\20 x - 20 y = 40\end{array} \right.$

The double line graph below shows the number of Acme Superstores vs. the number of General Superstores. -In what year was the number of Acme stores approximately equal to the number of General stores?

Solve the system of equations by the addition method. - $\left\{ \begin{array} { l } 8 x - 12 y = 14 \\- 2 x + 3 y = 0\end{array} \right.$

Answer true or false. -A system of two linear equations in two variables can have exactly two solutions.

Solve the system of equations by the addition method. - $\left\{ \begin{array} { l } 2 x + \frac { 2 } { 3 } y = - 16 \\2 x - \frac { 2 } { 3 } y = - 8\end{array} \right.$

Solve the problem by writing and using a system of linear equations. -A national wildlife refuge in Michigan has 104 thousand more trees than a national wildlife refuge in Ohio. The total number of trees for both is 308 thousand. Find the number of trees for each.

Solve the system of equations by the substitution method. - $\left\{ \begin{aligned}y & = 4 x + 2 \\3 y - 9 x & = 15\end{aligned} \right.$

Without graphing, decide: (a)Are the graphs of the equations are identical lines, parallel lines, or lines intersecting at a single point? (b)How many solutions does the system have? - $\left\{ \begin{array} { r } \frac { 1 } { 4 } x - y = 1 \\x = 4\end{array} \right.$

Solve the system of equations by graphing the equations on the same set of axes. - $\left\{ \begin{array} { l } y = x + 4 \\y = 3 x + 6\end{array} \right.$

Solve the problem. -A barge takes 4 hours to move (at a constant rate)downstream for 32 miles, helped by a current of 2 miles per hour. If the barge's engines are set at the same pace, find the time of its return trip against the current.

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

Decide whether or not the ordered pair satisfies the system of linear equations. -(4, -3); $\left\{ \begin{array} { l } 2 x = - 11 - y \\3 x = - 18 - 2 y\end{array} \right.$

Solve the system of equations by graphing the equations on the same set of axes. - $\left\{ \begin{array} { r } 2 x - y = 6 \\y = 2\end{array} \right.$

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

Decide whether or not the ordered pair satisfies the system of linear equations. -(-2, -6); $\left\{ \begin{array} { l } 3 x + y = 0 \\4 x + 3 y = 10\end{array} \right.$

Solve the problem. -Jarod is having a problem with rabbits getting into his vegetable garden, so he decides to fence it in. The length of the garden is 12 feet more than 6 times the width. He needs 136 feet of fencing to do the job. Find the length And width of the garden.

Solve the system of equations by the addition method. - $\left\{ \begin{array} { r } x - 5 y = - 26 \\6 x - 6 y = - 60\end{array} \right.$

Solve the system of equations by the addition method. - $\left\{ \begin{array} { l } \frac { x } { 5 } + \frac { y } { 10 } = 1 \\\frac { x } { 3 } - \frac { y } { 6 } = 0\end{array} \right.$