Exam 7: Systems of Equations

Solve the problem. -Helen Weller invested $\$ 10,000$ in an account that pays $12 \%$ simple interest. How much additional money must be invested in an account that pays 15\% simple interest so that the total interest is equal to the interest on the two investments at the rate of $13 \%$ ?

Solve by elimination. - $x+y=14$ $x-y=-2$

Solve the problem. -A private airplane leaves an airport and flies due east at $185 \mathrm{mph}$ . Two hours later, a jet leaves the same airport and flies due east at $333 \mathrm{mph}$ . When will the jet overtake the plane?

Solve by the substitution method. - $-4 \mathrm{x}-45=7 \mathrm{y}$ $2 \mathrm{x}+4 \mathrm{y}=-26$

Solve the problem. -Two cars leave town at the same time going in the same direction. One travels at $40 \mathrm{mph}$ and the other travels at $52 \mathrm{mph}$ . In how many hours will they be $48 \mathrm{mi}$ apart?

Solve by elimination. - $x+5 y=-25$ $6 x+6 y=-30$

Solve by elimination. - $1.3 x+4 y=-135.3$ $0)03 x-0.13 y=5.77$

Solve the problem. -Two angles are supplementary, and one is $5^{\circ}$ more than six times the other. Find the larger angle.

Solve the problem. -In a chemistry class, 5 liters of a $4 \%$ silver iodide solution must be mixed with a $10 \%$ solution to get a $6 \%$ solution. How many liters of the $10 \%$ solution are needed?

Solve the problem. -In a right triangle, one acute angle is $54^{\circ}$ more than twice the other. Find each acute angle.

Solve the system by graphing. - $4 x+y=-14$ $\mathrm{x}+4 \mathrm{y}=4$

Solve using the elimination method. - $5 \mathrm{x}-\mathrm{y}=17$ $-5 x+y=-17$

Solve the system by graphing. - $3 x+y=-10$ $5 x+3 y=-10$

Solve using the elimination method. - $3 x-y=17$ $4 \mathrm{x}+\mathrm{y}=25$

Decide whether or not the ordered pair is a solution of the system. - $(-5,2)$ $\mathrm{x}+\mathrm{y}=-3$ $\mathrm{x}-\mathrm{y}=-7$

Solve the system by graphing. -x + y = 7 X - y = -3

Solve the problem. -Two angles have a sum of $88^{\circ}$ . Their difference is $22^{\circ}$ . Find the angles.

Solve by the substitution method. - $x+y=5$ $4 \mathrm{x}+4 \mathrm{y}=20$

Solve the problem. -There were 33,000 people at a ball game in Los Angeles. The day's receipts were $\$ 245,000$ . How many people paid $\$ 13$ for reserved seats and how many paid $\$ 5$ for general admission?

Solve the problem. -Rachael's bike got a flat tire and she must walk the rest of the way to work. The bike was being ridden at $9 \mathrm{mph}$ , and Rachael walks at a speed of $4 \mathrm{mph}$ . The distanœ from home to work is $22 \mathrm{mi}$ , and the total time for the trip was $3 \mathrm{hr}$ . How far did she have to walk?