Exam 4: Solving Systems of Equations and Inequalities

Use two equations in two variables to solve the following problem. Maria and Susan pool their resources to buy several lottery tickets. They win $700,000! They agree that Susan should get $50,000 more than Maria, because she gave most of the money. How much will Maria get?

Solve the system by using either the substitution method or the elimination-by-addition method, whichever seems more appropriate. $\left( \begin{array} { c } \frac { 1 } { 2 } x - \frac { 1 } { 6 } y = - 12 \\\frac { 1 } { 2 } x + \frac { 1 } { 4 } y = 8\end{array} \right)$

In a mix of pennies and nickels, there are 22 coins with a total value of 82 cents. How many nickels are there?

The ordered pair (1, 3)is a solution of the given system. $\left\{ \begin{array} { l } 2 x + 2 y = 8 \\4 x + 3 y = 13\end{array} \right.$

Graph the solution of the system: $\left\{ \begin{array} { l } y < 5 x - 3 \\y - 5 x \geq 4\end{array} \right.$

Consider the following system: $\left\{ \begin{array} { c } 7 x + y = 54 \\y = - 7 x - 18\end{array} \right.$ Substitute $- 7 x - 18$ for y in the first equation. How many variables does the resulting equation contain?

Solve the system by graphing. $\left\{ \begin{array} { l } 4 x = 4 - 3 y \\4 x + 3 y = 7\end{array} \right.$

Use two equations in two variables to solve the following problem. At a theater, the giant rectangular movie screen has a width $24$ feet less than its length. If its perimeter is $308$ feet, find the area of the screen.

Melodic Music has compact discs on sale for either $15 or $20. If a customer wants to spend at least $60 but no more than $120 on CDs, graph a system of inequalities that will show the possible ways a customer can buy $15 CDs ( x )and $20 CDs ( y ).

Use the addition method to solve the system. $\left\{ \begin{array} { c } a + b = 5 \\a - b = - 1\end{array} \right.$

Determine whether the ordered pair is a solution of the system of equations shown below. Ordered pair $( 2,4 )$ System of equations $x - y = - 2$ $3 x + 2 y = 14$

Solve the system by any method, if possible. $\left\{ \begin{array} { l } x = \frac { 3 } { 2 } y + 3 \\2 x - 3 y = 9\end{array} \right.$

Solve the system by elimination if possible. $\left\{ \begin{array} { c } 2 x + 3 y = 29 \\3 x - 2 y = - 15\end{array} \right.$

Find the solution set of the system of inequalities. $\left\{ \begin{array} { l } x + y < - 6 \\x - y > - 6\end{array} \right.$

A gift store is making a mixture of almonds, pecans, and peanuts, which sell for $3.00 per pound, $4.00 per pound, and $2.00 per pound, respectively. The storekeeper wants to make 20 pounds of the mix to sell at $2.70 per pound. The number of pounds of peanuts is to be three times the number of pounds of pecans. Find the number of pounds of each to be used in the mixture. # of almonds = __________ # of pecans = __________ # of peanuts = __________

Use the substitution method to solve the following system: $\left\{ \begin{array} { l } 2 x = \frac { 1 } { 2 } y - 1.2 \\\frac { 1 } { 5 } y = 6 x - 1.6\end{array} \right.$

Tell whether the ordered pair (- 5, 3)is a solution of the given system. $\left\{ \begin{array} { l } - 3 x + 8 y = 36 \\4 x - 5 y = - 31\end{array} \right.$

Doris invested some money at 7% and some money at 8%. She invested $4,000 more at 8% than she did at 7%. Her total yearly interest from the two investments was $920. How much did Doris invest at each rate?

Solve the system. $\left\{ \begin{array} { c } x + 4 y = - 4 \\x - 4 y = - 12\end{array} \right.$

Use the addition method to solve the system. If the equations of the system are dependent, or if a system is inconsistent, so indicate. $\left\{ \begin{array} { l } 2 ( x + 2 ) + 9 ( y - 4 ) = 1 \\2 ( x - 1 ) = - 9 ( y + 2 )\end{array} \right.$