Exam 10: Systems of Linear Equations

A projectile is launched from the ground. Its height (metres) after $t$ seconds is given by $s=k t^{2}+v_{0} t$ where $k$ is a constant, $v_{0}$ is the initial velocity. If the height at $1.0 \mathrm{~s}$ is $8.7 \mathrm{~m}$ and the height at $1.5 \mathrm{~s}$ is $7.625 \mathrm{~m}$ , determine the height at time $2.0 \mathrm{~s}$ .

Solve for $x, y$ , and $z: a x+b y=c x y$ $a x-c z=b x z$ $b y+c z=a y z$

Number $A$ divided by number $B$ equals one-fourth. Number $B$ divided by number $A$ equals two times number $A$ . What are the two numbers?

Find the approximate solution by graphing: $2 x+4 y=4$ $3 x-5 y=-5$

Solve: 0.2x + 0.2y + 0.2z = 7.0 0.2x − 0.4y + 0.6z = 3.0 0.2x - 0.2y + 0.2z = −1.0

Runner $Y$ leaves the starting line at 12:00. Five minutes later runner $X$ leaves from the same place and catches up to runner $Y$ at 12:07. Four minutes later, runner $X$ is one hundred metres ahead of runner $Y$ . What is the speed of each runner in $\mathrm{m} / \mathrm{s}$ ?

Find the approximate solution by graphing: $x+3 y=-5$ $2 x-y=10$

Solve simultaneously: $\frac{3}{x}-\frac{6}{y}=2$ $\frac{5}{x}+\frac{10}{y}=10$

Solve simultaneously: $\frac{10}{x}+\frac{45}{y}=-4$ $\frac{26}{x}+\frac{10}{y}=11$

A lab technician wants to mix some amount of a $15 \%$ acid solution and another amount of a $25 \%$ acid solution so that his resultant mixture is $8 \overline{0} \mathrm{ml}$ of a $22 \%$ acid solution. What volume of the $15 \%$ acid solution and $25 \%$ acid solution is required?

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

Solve by any algebraic method: $8 x+7 y=-23$ $3 x+5 y=8$

Solve by any method: $3 x+4 y=72$ $4 x-3 y=21$

Solve by any algebraic method: $9 x-5 y=8$ $3 x+4 y=14$

Solve: $5 x-y=14$ $10 z-y=12$ $x+5 z=20$

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

Solve. Leave your answers in fractional form: $\frac{1}{x}+\frac{1}{y}-\frac{1}{z}=5$ +=6 +-=5

Solve simultaneously: $x+\frac{2 x-y+1}{9 y}=\frac{-16}{9}$ $\frac{x-3 y+1}{2}-\frac{x-2 y}{3}=1$

A horizontal beam of negligible weight is simply supported at each end by columns. When a vertical load as placed on a beam $1.00 \mathrm{~m}$ from the left end, the vertical upward reaction is the right column is $62.5 \mathrm{~N}$ . When the load is increased by $40.0 \mathrm{~N}$ , the reaction in the right column increases to $75.0 \mathrm{~N}$ . How long is the beam?

Solve: $x+2 y-z=4$ 2x-y-3z=-19 x+5y+2z=25