Exam 4: Systems of Equations

A student took out two loans totaling $\$ 15,000$ to help pay for college expenses. One loan was at $10 \%$ simple interest, and the other was at $5 \%$ . After one year, the student owed $\$ 1250$ in interest. Find the amount of the loan at $5 \%$ .

Is the ordered triple a solution to the given system of equations? - $(2,9,-4)$ 2x-5y-9z=-5 X+y+z=7 3x-y+5z=35

The sum of two angles is $136^{\circ}$ . One angle is $20^{\circ}$ less than twice the other. Find the angles.

A $\$ 134,000$ trust is to be invested in bonds paying $7 \%$ , CDs paying $6 \%$ , and mortgages paying $10 \%$ . The bond and CD investment together must equal the mortgage investment. To earn a $\$ 11,130$ annual income from the investments, how much should the bank invest in bonds?

Michael's bank contains only nickels, dimes, and quarters. There are 62 coins in all, valued at $\$$ 5.20. The number of nickels is 10 short of being three times the sum of the number of dimes and quarters together. How many dimes are in the bank?

Draw the graph of a linear equation that, along with the given line, forms a dependent system.

$3 x+3 y+z=-19$ $4 x-2 y-z=-18$ $5 \mathrm{x}+\mathrm{y}+3 \mathrm{z}=-21$

Solve the system using the addition method. If the system is inconsistent and has no solution, state this. If the system is dependent, write the form of the solution for any real number $x$ . - $0.9 x+0.2 y=4.2$ $\mathrm{x}-0.1 \mathrm{y}=3.7$

Set up a system of equations, and use it to balance the chemical equation for the given reaction. - $\mathrm{C}_{2} \mathrm{H}_{2}$ and $\mathrm{O}_{2}$ react to produce $\mathrm{CO}_{2}$ and $\mathrm{H}_{2} \mathrm{O}$ .

A retired couple invested a total of $\$ 160,000$ . They invested some of the money in safe certificates of deposit yielding $7 \%$ . The remainder they invested in AA bonds yielding $10 \%$ per year. In the first year they made a total profit of $\$ 14,200$ . How much did they invest at each rate?

$5 x+2 y+z=-11$ $2 x-3 y-z=17$ $7 \mathrm{x}+\mathrm{y}+2 \mathrm{z}=-4$

If a plane can travel 210 miles per hour with the wind and only 190 miles per hour against the wind, find the speed of the wind and the speed of the plane in still air.

Solve the system using the addition method. If the system is inconsistent and has no solution, state this. If the system is dependent, write the form of the solution for any real number $x$ . - $x+y=11$ $\mathrm{x}-\mathrm{y}=3$

Solve by addition or substitution. - $x-2 y=-7$ $2 \mathrm{x}-3 \mathrm{y}=-13$

Is the ordered pair a solution of the given system of equations? - left parenthesis3comma3right parenthesiscomma x+y=0 x-y=-6

Solve the system of equations using matrices. - $-3 x+4 y=-5$ $12 x-7 y=-25$

Graph the system of inequalities. - x >2 y \leq-2

A rectangular print has a perimeter of 62 inches. The length is 11 inches greater than the width. Find the width of the print.

Solve the system of equations using matrices. - $x+8 y=8$ $4 \mathrm{x}-7 \mathrm{y}=-7$

Solve the system of equations using Cramer's rule. - $8 x-3 y+6 z=65$ $2 x+7 y-5 z=-15$ $8 \mathrm{x}-2 \mathrm{y}+2 \mathrm{z}=42$