Exam 10: Systems of Linear Equations

A person invested $\$ 5,200$ , part in bonds bearing $5.9 \%$ interest and the remainder in bonds bearing $7.6 \%$ interest. Both investments paid the same amount after the same period of time. How much, to the nearest dollar, was invested in each?

Solve: $x+2 z=5$ $3 x+4 y=2$ $3 y-2 z=3$

Solve simultaneously: $\frac{x}{4}+\frac{y}{5}=18$ $\frac{x}{6}-\frac{y}{3}=-2$

Solve simultaneously. Leave your answers in fractional form: $\frac{1}{x}+\frac{1}{y}=\frac{3}{5}$ $\frac{2}{x}+\frac{4}{y}=4$

The sum of the digits of a two-digit number is 12 . When the digits are reversed, the number is increased by 18 . Find the number.

Solve: $0.50 x+1.0 y+1.5 z=7.0$ $1.0 x+0.50 y+1.0 z=5.0$ $1.5 x+2.0 y+1.5 z=1.0$

Find the approximate solution by graphing: $5 x-2 y=9$ $-3 x+3 y=9$

Solve by any method: $2 x-5 y=38$ $y=3 x-18$

The sum of two numbers is twenty-one and their difference is fifteen. What are the numbers?

Solve: $3 x-z=0$ $y+z=2$ $x+y=5$

A chemist has two acid solutions, one that contains $14.0 \%$ acid and another with $27.0 \%$ acid. How many litres of each must be mixed to make 250 litres of solution containing $17.64 \%$ acid?

Solve simultaneously: $\frac{x}{7}+\frac{y}{24}=\frac{15}{2}$ $\frac{y}{10}+2 x=76$

Solve: $x+\frac{y}{2}-\frac{z}{3}=21$ +y-=19 +-z=26

Solve: $2 y+3 x=50$ $x+4 z=30$ $2 z+3 y=20$

Solve for $x$ and $y$ in terms of the other literal quantities: $a x+b y=4$ $a x-d y=2$