Exam 11: Systems of Equations

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

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { l } 2 x + y = 7 \\6 x + 3 y = 21\end{array} \right.$

Solve the system of equations by the addition method. - $\left\{ \begin{array} { l } - 6 x - 6 y = - 6 \\12 x + 12 y = 12\end{array} \right.$

Solve the system of equations by graphing the equations on the same set of axes. - $\left\{ \begin{array} { l } y = x - 1 \\y = - 2 x + 8\end{array} \right.$

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { l } - 9 y = x - 79 \\2 x + 8 y = 68\end{array} \right.$

Solve the problem. -Devon purchased tickets to an air show for 5 adults and 2 children. The total cost was $167. The cost of a child's ticket was $4 less than the cost of an adult's ticket. Find the price of an adult's ticket and a child's ticket.

Without solving, choose the correct solution by deciding which choice satisfies the given conditions. -At the local convenience store, 3 bags of chips and 4 containers of dip cost $25. However, 4 bags of chips and 7 containers of dip cost $40. What is the cost of one bag of chips and one container of dip?

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { l } - 3 x + y = 28 \\- 4 x + 7 y = 77\end{array} \right.$

Solve the system of equations by the addition method. - $\left\{ \begin{array} { l } 5 x + y = - 18 \\6 x - y = 7\end{array} \right.$

Solve the system of equations by graphing the equations on the same set of axes. - $\left\{ \begin{array} { c } x - 2 y = 1 \\3 x + 2 y = - 13\end{array} \right.$

Write a system of equations to describe the situation. Do not solve the system. -An order of 4 orders of fries, 3 hamburgers, and 5 drinks costs $15. An order of 4 orders of fries, 3 hamburgers, and 2 drinks costs $12. All drinks are $1.

Solve the system of equations by the addition method. - $\left\{ \begin{array} { l } 3 x - 5 y = - 10 \\5 x - 4 y = - 21\end{array} \right.$

Decide whether or not the ordered pair satisfies the system of linear equations. -(3, -1); $\left\{ \begin{array} { l } 3 x = 8 - y \\2 x = 3 - 3 y\end{array} \right.$

Solve the problem. -Jamil always throws loose change into a pencil holder on his desk and takes it out every two weeks. This time it is all nickels and dimes. There are 3 times as many dimes as nickels, and the value of the dimes is $1.75 more Than the value of the nickels. How many nickels and dimes does Jamil have?

Solve the system of equations by the addition method. - $\left\{ \begin{array} { l } x + y = - 6 \\x + y = - 8\end{array} \right.$

Solve the system by the substitution or the addition method. - $\left\{ \begin{array} { l } 0.04 x - 0.06 y = - 0.22 \\0.2 x + 0.4 y = - 0.4\end{array} \right.$

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? - $\left\{ \begin{aligned}y - 2 x & = 3 \\6 y & = 12 x + 18\end{aligned} \right.$

Solve the system of equations by the substitution method. - $\left\{ \begin{array} { l } \frac { 1 } { 7 } x - 2 y = 1 \\x - 14 y = 7\end{array} \right.$

The double line graph below shows the number of Acme Superstores vs. the number of General Superstores. -In what years was the number of Acme stores greater than the number of General stores?

Solve the problem. -Natasha rides her bike (at a constant speed)for 3 hours, helped by a wind of 3 miles per hour. Pedaling at the same rate, the trip back against the wind takes 9 hours. Find find the total round trip distance she traveled.