Question 1

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

Accepted Answer

The answer of Solve: 0.2x + 0.2y + 0.2z =...

Question 2

Solve. Leave your answers in fractional form: $\frac{1}{x}+\frac{2}{z}=7$
$\begin{array}{r}
\frac{1}{y}+\frac{1}{z}=\frac{7}{2} \
\frac{4}{x}-\frac{1}{y}+\frac{4}{z}=20
\end{array}$

Accepted Answer

The answer of Solve. Leave your answers in fractional form:...

Question 3

Solve. Leave your answers in fractional form: $\frac{x}{3}+\frac{y}{2}+\frac{z}{4}=1$
$\begin{array}{r}
2 x+3 y+2 z=4 \
x+\frac{y}{3}+\frac{z}{2}=2
\end{array}$

Accepted Answer

The answer of Solve. Leave your answers in fractional form:...

Question 4

Solve: $x+z=5 a$
$\begin{array}{r}
y-z=-6 a \
2 x+3 y=-4 a
\end{array}$

Accepted Answer

The answer of Solve: $x+z=5 a$
\(\begin{array}{r}
y-z=-6 a \
2 x+3 y=-4...

Question 5

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

Accepted Answer

The answer of Solve for $x, y$, and \(z: a...

Question 6

Solve. Leave your answers in fractional form: $\frac{1}{x}+\frac{1}{y}-\frac{1}{z}=5$
$\begin{aligned}
& \frac{1}{x}+\frac{1}{z}=6 \
& \frac{-1}{x}+\frac{3}{y}-\frac{5}{z}=5
\end{aligned}$

Accepted Answer

The answer of Solve. Leave your answers in fractional form:...

Question 7

Solve. Leave your answers in fractional form: $\frac{1}{x}+\frac{2}{y}-\frac{2}{z}=6$
$\begin{aligned}
& \frac{1}{x}+\frac{1}{y}=7 \
& \frac{2}{y}-\frac{1}{z}=3
\end{aligned}$

Accepted Answer

The answer of Solve. Leave your answers in fractional form:...

Question 8

Solve: $\frac{x}{3}-\frac{y}{2}+\frac{z}{6}=-4$
$\begin{gathered}
\frac{2 x}{3}+\frac{4 y}{3}-\frac{z}{2}=29 \
\frac{x}{2}+\frac{y}{3}-\frac{z}{6}=11
\end{gathered}$

Accepted Answer

The answer of Solve: $\frac{x}{3}-\frac{y}{2}+\frac{z}{6}=-4$
$\begin{gathered}
\frac{2 x}{3}+\frac{4 y}{3}-\frac{z}{2}=29 \
\frac{x}{2}+\frac{y}{3}-\frac{z}{6}=11
\end{gathered}$...

Question 9

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

Accepted Answer

The answer of Solve: $x+\frac{y}{2}-\frac{z}{3}=21$
$\begin{aligned}
& \frac{x}{3}+y-\frac{z}{2}=19 \
& \frac{x}{2}+\frac{y}{3}-z=26
\end{aligned}$...

Question 10

Solve: $\frac{2 x+5}{3}-\frac{y-1}{2}+z=11$
$\begin{aligned}
& \frac{x+6}{4}+y+\frac{z+1}{6}=11 \
& x-\frac{y+2}{3}-\frac{z-1}{2}=-6
\end{aligned}$

Accepted Answer

The answer of Solve: $\frac{2 x+5}{3}-\frac{y-1}{2}+z=11$
$\begin{aligned}
& \frac{x+6}{4}+y+\frac{z+1}{6}=11 \
& x-\frac{y+2}{3}-\frac{z-1}{2}=-6
\end{aligned}$...

Question 11

Solve: $\frac{x-1}{y-2}=\frac{4}{5}$
$\begin{aligned}
& \frac{x+2}{z-3}=\frac{7}{3} \
& \frac{y-1}{z+2}=\frac{3}{4}
\end{aligned}$

Accepted Answer

The answer of Solve: $\frac{x-1}{y-2}=\frac{4}{5}$
$\begin{aligned}
& \frac{x+2}{z-3}=\frac{7}{3} \
& \frac{y-1}{z+2}=\frac{3}{4}
\end{aligned}$...

Question 12

The sum of the digits of a certain three-digit number is nine. The sum of the hundreds and the tens digits is equal to the ones digit minus one. The number, divided by nine, equals three times the ones digit. What is the number?

Accepted Answer

The answer of The sum of the digits of a...

Question 13

A certain number has three digits and the sum of those digits 12 . When the number is divided by the number formed by the hundreds and the ones digits, the answer equals 11 . In addition, the sum of the hundreds and the tens digits is 10 bigger than the ones digit. What is the number?

Accepted Answer

The answer of A certain number has three digits and...

Question 14

The atomic mass of three compounds are known: methane $\left(\mathrm{CH}_{4}\right)$ is 16.0 , glycerol $(\mathrm{C} 3 \mathrm{H} 8 \mathrm{O} 3)$ is 91.9 , and water $(\mathrm{H} 2 \mathrm{O})$ is 18.0. Calculate the atomic mass of $\mathbf{C}, \mathbf{H}$, and $\mathbf{O}$ by solving this linear system:
$\mathbf{C}+4 \mathbf{H}=16.0$
$\begin{array}{r}
3 \mathrm{C}+8 \mathrm{H}+3 \mathrm{O}=91.9 \
2 \mathbf{H}+\mathbf{O}=18.0
\end{array}$

Accepted Answer

The answer of The atomic mass of three compounds are...

Question 15

A projectile is launched from height $h_{o}$ above the ground. Its height (metres) after $t$ seconds is given by $s=k t^{2}+v_{0} t+h_{0}$ where $k$ is a constant, $v_{0}$ is the initial velocity. If the height at $1.0 \mathrm{~s}$ is $7.75 \mathrm{~m}$ and the height at $1.5 \mathrm{~s}$ is $6.625 \mathrm{~m}$, and the height at $2.0 \mathrm{~s}$ is $5.00 \mathrm{~m}$, determine the height at time $2.5 \mathrm{~s}$.

Accepted Answer

The answer of A projectile is launched from height $h_{o}$...

Quiz 10: Systems of Linear Equations

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

Solve. Leave your answers in fractional form: $\frac{1}{x}+\frac{2}{z}=7$ $\begin{array}{r}\frac{1}{y}+\frac{1}{z}=\frac{7}{2} \\\frac{4}{x}-\frac{1}{y}+\frac{4}{z}=20\end{array}$

Solve. Leave your answers in fractional form: $\frac{x}{3}+\frac{y}{2}+\frac{z}{4}=1$ $\begin{array}{r}2 x+3 y+2 z=4 \\x+\frac{y}{3}+\frac{z}{2}=2\end{array}$

Solve: $x+z=5 a$ $\begin{array}{r}y-z=-6 a \\2 x+3 y=-4 a\end{array}$

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

Solve. Leave your answers in fractional form: $\frac{1}{x}+\frac{1}{y}-\frac{1}{z}=5$ $\begin{aligned}& \frac{1}{x}+\frac{1}{z}=6 \\& \frac{-1}{x}+\frac{3}{y}-\frac{5}{z}=5\end{aligned}$

Solve. Leave your answers in fractional form: $\frac{1}{x}+\frac{2}{y}-\frac{2}{z}=6$ $\begin{aligned}& \frac{1}{x}+\frac{1}{y}=7 \\& \frac{2}{y}-\frac{1}{z}=3\end{aligned}$

Solve: $\frac{x}{3}-\frac{y}{2}+\frac{z}{6}=-4$ $\begin{gathered}\frac{2 x}{3}+\frac{4 y}{3}-\frac{z}{2}=29 \\\frac{x}{2}+\frac{y}{3}-\frac{z}{6}=11\end{gathered}$

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

Solve: $\frac{2 x+5}{3}-\frac{y-1}{2}+z=11$ $\begin{aligned}& \frac{x+6}{4}+y+\frac{z+1}{6}=11 \\& x-\frac{y+2}{3}-\frac{z-1}{2}=-6\end{aligned}$

Solve: $\frac{x-1}{y-2}=\frac{4}{5}$ $\begin{aligned}& \frac{x+2}{z-3}=\frac{7}{3} \\& \frac{y-1}{z+2}=\frac{3}{4}\end{aligned}$

The sum of the digits of a certain three-digit number is nine. The sum of the hundreds and the tens digits is equal to the ones digit minus one. The number, divided by nine, equals three times the ones digit. What is the number?

A certain number has three digits and the sum of those digits 12 . When the number is divided by the number formed by the hundreds and the ones digits, the answer equals 11 . In addition, the sum of the hundreds and the tens digits is 10 bigger than the ones digit. What is the number?

Quiz 10: Systems of Linear Equations

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

Solve. Leave your answers in fractional form: 1x+2z=7\frac{1}{x}+\frac{2}{z}=7x1​+z2​=7 1y+1z=724x−1y+4z=20\begin{array}{r}\frac{1}{y}+\frac{1}{z}=\frac{7}{2} \\\frac{4}{x}-\frac{1}{y}+\frac{4}{z}=20\end{array}y1​+z1​=27​x4​−y1​+z4​=20​

Solve. Leave your answers in fractional form: x3+y2+z4=1\frac{x}{3}+\frac{y}{2}+\frac{z}{4}=13x​+2y​+4z​=1 2x+3y+2z=4x+y3+z2=2\begin{array}{r}2 x+3 y+2 z=4 \\x+\frac{y}{3}+\frac{z}{2}=2\end{array}2x+3y+2z=4x+3y​+2z​=2​

Solve: x+z=5ax+z=5 ax+z=5a y−z=−6a2x+3y=−4a\begin{array}{r}y-z=-6 a \\2 x+3 y=-4 a\end{array}y−z=−6a2x+3y=−4a​

Solve for x,yx, yx,y , and z:ax+by=cxyz: a x+b y=c x yz:ax+by=cxy ax−cz=bxza x-c z=b x zax−cz=bxz by+cz=ayzb y+c z=a y zby+cz=ayz

Solve. Leave your answers in fractional form: 1x+1y−1z=5\frac{1}{x}+\frac{1}{y}-\frac{1}{z}=5x1​+y1​−z1​=5 1x+1z=6−1x+3y−5z=5\begin{aligned}& \frac{1}{x}+\frac{1}{z}=6 \\& \frac{-1}{x}+\frac{3}{y}-\frac{5}{z}=5\end{aligned}​x1​+z1​=6x−1​+y3​−z5​=5​

Solve. Leave your answers in fractional form: 1x+2y−2z=6\frac{1}{x}+\frac{2}{y}-\frac{2}{z}=6x1​+y2​−z2​=6 1x+1y=72y−1z=3\begin{aligned}& \frac{1}{x}+\frac{1}{y}=7 \\& \frac{2}{y}-\frac{1}{z}=3\end{aligned}​x1​+y1​=7y2​−z1​=3​

Solve: x3−y2+z6=−4\frac{x}{3}-\frac{y}{2}+\frac{z}{6}=-43x​−2y​+6z​=−4 2x3+4y3−z2=29x2+y3−z6=11\begin{gathered}\frac{2 x}{3}+\frac{4 y}{3}-\frac{z}{2}=29 \\\frac{x}{2}+\frac{y}{3}-\frac{z}{6}=11\end{gathered}32x​+34y​−2z​=292x​+3y​−6z​=11​

Solve: x+y2−z3=21x+\frac{y}{2}-\frac{z}{3}=21x+2y​−3z​=21 x3+y−z2=19x2+y3−z=26\begin{aligned}& \frac{x}{3}+y-\frac{z}{2}=19 \\& \frac{x}{2}+\frac{y}{3}-z=26\end{aligned}​3x​+y−2z​=192x​+3y​−z=26​

Solve: 2x+53−y−12+z=11\frac{2 x+5}{3}-\frac{y-1}{2}+z=1132x+5​−2y−1​+z=11 x+64+y+z+16=11x−y+23−z−12=−6\begin{aligned}& \frac{x+6}{4}+y+\frac{z+1}{6}=11 \\& x-\frac{y+2}{3}-\frac{z-1}{2}=-6\end{aligned}​4x+6​+y+6z+1​=11x−3y+2​−2z−1​=−6​

Solve: x−1y−2=45\frac{x-1}{y-2}=\frac{4}{5}y−2x−1​=54​ x+2z−3=73y−1z+2=34\begin{aligned}& \frac{x+2}{z-3}=\frac{7}{3} \\& \frac{y-1}{z+2}=\frac{3}{4}\end{aligned}​z−3x+2​=37​z+2y−1​=43​​

The sum of the digits of a certain three-digit number is nine. The sum of the hundreds and the tens digits is equal to the ones digit minus one. The number, divided by nine, equals three times the ones digit. What is the number?

A certain number has three digits and the sum of those digits 12 . When the number is divided by the number formed by the hundreds and the ones digits, the answer equals 11 . In addition, the sum of the hundreds and the tens digits is 10 bigger than the ones digit. What is the number?

Solve. Leave your answers in fractional form: $\frac{1}{x}+\frac{2}{z}=7$ $\begin{array}{r}\frac{1}{y}+\frac{1}{z}=\frac{7}{2} \\\frac{4}{x}-\frac{1}{y}+\frac{4}{z}=20\end{array}$

Solve. Leave your answers in fractional form: $\frac{x}{3}+\frac{y}{2}+\frac{z}{4}=1$ $\begin{array}{r}2 x+3 y+2 z=4 \\x+\frac{y}{3}+\frac{z}{2}=2\end{array}$

Solve: $x+z=5 a$ $\begin{array}{r}y-z=-6 a \\2 x+3 y=-4 a\end{array}$

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

Solve. Leave your answers in fractional form: $\frac{1}{x}+\frac{1}{y}-\frac{1}{z}=5$ $\begin{aligned}& \frac{1}{x}+\frac{1}{z}=6 \\& \frac{-1}{x}+\frac{3}{y}-\frac{5}{z}=5\end{aligned}$

Solve. Leave your answers in fractional form: $\frac{1}{x}+\frac{2}{y}-\frac{2}{z}=6$ $\begin{aligned}& \frac{1}{x}+\frac{1}{y}=7 \\& \frac{2}{y}-\frac{1}{z}=3\end{aligned}$

Solve: $\frac{x}{3}-\frac{y}{2}+\frac{z}{6}=-4$ $\begin{gathered}\frac{2 x}{3}+\frac{4 y}{3}-\frac{z}{2}=29 \\\frac{x}{2}+\frac{y}{3}-\frac{z}{6}=11\end{gathered}$

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

Solve: $\frac{2 x+5}{3}-\frac{y-1}{2}+z=11$ $\begin{aligned}& \frac{x+6}{4}+y+\frac{z+1}{6}=11 \\& x-\frac{y+2}{3}-\frac{z-1}{2}=-6\end{aligned}$

Solve: $\frac{x-1}{y-2}=\frac{4}{5}$ $\begin{aligned}& \frac{x+2}{z-3}=\frac{7}{3} \\& \frac{y-1}{z+2}=\frac{3}{4}\end{aligned}$