Exam 4: Systems of Linear Equations

Solve the problem using a system of equations. -Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 99 miles in the same time that Dana travels 87 miles. If Chuck's rate of travel is $4 \mathrm{mph}$ more than Dana's, then at what rate does Chuck travel?

The solution set of the system $y_{1}=-x+5$ and $y_{2}=-2 x+7$ is $\{(2,3)\}$ . Using slopes and $y$ -intercepts, determine which of the two calculator-generated screens, left or right, is the appropriate one for this system.

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. - $y=x-6$ $y=-x+16$

Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $\$ 105.00$ for 3 days and 300 miles, while Mary was charged $\$ 195.00$ for 5 days and 600 miles. What does Best Rentals charge per day and per mile?

Tell how many solutions the system has. Do not actually solve. - $3 x=y+3$ $6 x-2 y=3$

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. - $x+y=9$ $5 x+5 y=45$

$3 x+2 y=2$ $3 x-6 z=-9$ $6 y-3 z=5$

Solve the system of equations. - $\frac{6}{y}+\frac{2}{x}=\frac{23}{20}$ $\frac{4}{y}-\frac{2}{x}=\frac{1}{10}$

Emilia doesn't trust banks, so her savings are hidden under her mattress. Deepak has his savings in an investment at simple interest. During which year did they have the same amount?

A company manufactures three products. The graph shows the production from 1986 to 1996. Which of the companies experience production growth over the period shown in the graph?

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so. - $2 x-3 y=-2$ $6 x-9 y=6$

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. - $-2 x+3 y=-1$ $3 x+2 y=21$

Decide whether the ordered pair is a solution of the given system - $4 x+y=25$ $2 \mathrm{x}+4 \mathrm{y}=16 ;(6,1)$

In triangle $A B C$ , the measure of angle $B$ is $5^{\circ}$ more than three times the measure of angle $A$ . The measure of angle $\mathrm{C}$ is $15^{\circ}$ more than the measure of angle $\mathrm{A}$ . What is the measure of Angle $\mathrm{C}$ ?

Solve the system by elimination. If the system is inconsistent or has dependent equations, say so. - $\frac{1}{5} x-\frac{1}{4} y=1$ $\frac{2}{5} x+\frac{1}{2} y=2$

From a point on a river, two boats are driven in opposite directions, one at 10 miles per hour and the other at 11 miles per hour. In how many hours will they be 63 miles apart?

An airplane travels 800 miles against the wind in 5 hours, and makes the return trip with the same wind in 2 hours. Find the rate of the wind.

Solve the system. Express the solution in the form $(x, y, z, w)$ . - 6x-2z+w =-22 -x+y+4z-w =-8 2x-y+4w =-13 Y+6z-w =-21

Solve the system. Express the solution in the form $(x, y, z, w)$ . - $2 x-2 z+w=-1$ -x+2y+z-2w =0 5x-y+2w =14 y-2z-w =-3

Solve the system by substitution. If the system is inconsistent or has dependent equations, say so. - $5 x+y=30$ $-x+y=-12$