Exam 4: Solving Systems of Linear Equations

Solve the system. - $\left\{ \begin{array} { r r } x - y + 5 z & = - 2 \\3 x + z & = 0 \\x + 3 y + z & = 6\end{array} \right.$

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

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

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? - $\left\{ \begin{aligned}x + 6 y & = 18 \\y & = - \frac { 1 } { 6 } x + 3\end{aligned} \right.$

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? - $\left\{ \begin{array} { l } 5 x + y = - 12 \\2 x + 2 y = 0\end{array} \right.$

Solve. -Jimmy is a partner in an Internet-based coffee supplier. The company offers gourmet coffee beans for $\$ 13$ per pound and regular coffee beans for $\$ 4$ per pound. Jimmy is creating a medium-price product that will sell for $\$ 6$ per pound. The first thing to go into the mixing bin was 20 pounds of the gourmet beans. How many pounds of the less expensive regular beans should be added?

Write a system of equations in x and y describing the situation. Do not solve the system. -One number is 5 more than another number. If you add 8 to 3 times the first number, the result is 4 times the second number.

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 or more linear equations are called a(n)_________

Solve the system of equations by graphing. - $\left\{ \begin{aligned}x + 3 y & = - 7 \\2 x - 3 y & = 4\end{aligned} \right.$

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? - $\left\{ \begin{array} { r } 5 x - y = 26 \\x + 5 y = 26\end{array} \right.$

Solve the system of equations by the substitution method. - $\left\{ \begin{aligned}4 x - 2 y & = 70 \\x & = 3 y\end{aligned} \right.$

Solve the system. - $\left\{ \begin{array} { r } y + 5 z = - 8 \\- 4 x + y - 3 z = 8 \\2 x + 3 z = - 7\end{array} \right.$

Solve. -On a buying trip in Los Angeles, Rosaria Perez ordered 120 pieces of jewelry: a number of bracelets at $\$ 7$ each and a number of necklaces at $\$ 9$ each. She wrote a check for $\$ 1040$ to pay for the order. How many bracelets and how many necklaces did Rosaria purchase?

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question. -At the break-even point both cost and revenue are what?

Is the ordered pair a solution of the linear system? - $\left\{ \begin{array} { l } 3 x - 3 y = 12 \\6 x + y = 1\end{array} ; ( 2 , - 2 ) \right.$

Solve the system of equations by the addition method. - $\left\{ \begin{array} { r } 4 x + 6 y = 76 \\- 2 x - 6 y = - 86\end{array} \right.$

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

Determine whether the ordered pair is a solution of the system of linear equations. - (-2,9); 2x=6-y x+3y=25

Given the cost function, C(x), and the revenue function, R(x), find the number of units x that must be sold to break even. - C(x)=1.3x+1400 R(x)=2.3x

Although $( 1,10 )$ is not a solution of $x + 5 y = 2$ , it can still be a solution of the system $\left\{ \begin{array} { l } x + 5 y = 2 \\ x + y = 2 \end{array} \right.$ .