Exam 13: Systems of Equations

Solve the problem. -Candy and Delvis are riding bicycles in the same direction. Candy is traveling at the speed of 8 miles per hour, and Delvis is traveling at the speed of 13 miles per hour. In 5 hours what is the distance between them?

Solve the problem. -The perimeter of a rectangle is $52 \mathrm{~m}$ . If the width were doubled and the length were increased by $24 \mathrm{~m}$ , the perimeter would be $114 \mathrm{~m}$ . What are the length and width of the rectangle?

Solve using the elimination method. - $-x-5 y=-34$ $2 x+5 y=28$

Solve by the substitution method. - $5 x+9 y=-15$ $3 x+6 y=-9$

Decide whether or not the ordered pair is a solution of the system. - $(6,-4)$ $2 \mathrm{x}+\mathrm{y}=8$ $3 x+2 y=10$

Solve the problem. -A private airplane leaves an airport and flies due east at $175 \mathrm{mph}$ . Two hours later, a jet leaves the same airport and flies due east at $315 \mathrm{mph}$ . When will the jet overtake the plane?

Decide whether or not the ordered pair is a solution of the system. - $(-4,-3)$ $\mathrm{x}+\mathrm{y}=-7$ $x-y=-1$

Solve the problem. -Roberto invested some money at $7 \%$ , and then invested $\$ 4000$ more than twice this amount at $12 \%$ . His total annual income from the two investments was $\$ 3890$ . How much was invested at $12 \%$ ?

Solve by elimination. - $6 x+9 y=27$ $4 x-6 y=-18$

Solve by elimination. - $4 x+8 y=-8$ $2 \mathrm{x}-2 \mathrm{y}=-4$

Solve the system by graphing. - $4 x+y=-11$ $3 x+6 y=18$

Solve the problem. -How many liters of a $10 \%$ alcohol solution must be mixed with 60 liters of a $70 \%$ solution to get a $60 \%$ solution?

Solve the problem. -Ellen wishes to mix candy worth $\$ 1.69$ per pound with candy worth $\$ 3.50$ per pound to form 28 pounds of a mixture worth $\$ 2.21$ per pound. How many pounds of the more expensive candy should she use?

Solve by elimination. - $x-\frac{2}{3} y=\frac{89}{12}$ $\frac{2}{3} x+y=-\frac{19}{2}$

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

Solve the problem. -A plane flies 500 miles with the wind and 300 miles against the wind in the same length of time. If the speed of the wind is $21 \mathrm{mph}$ , what is the speed of the plane in still air?

Solve the problem. -The perimeter of a triangle is $60 \mathrm{~cm}$ . The triangle is isosceles now, but if its base were lengthened by $3 \mathrm{~cm}$ and each leg were shortened by $6 \mathrm{~cm}$ , it would be equilateral. Find the base of the original triangle.

Solve by elimination. - $x+5 y=-9$ $2 x+5 y=-3$

Solve by the substitution method. - $8 x+5 y=-25$ $4 x+3 y=-15$