Solve for x
x=\frac{45y}{46}+\frac{225z}{23}-\frac{18}{23}
Solve for y
y=\frac{46x}{45}-10z+\frac{4}{5}
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101x+80+100z+10y+x=1000z+100y+10x+8
Combine 100x and x to get 101x.
102x+80+100z+10y=1000z+100y+10x+8
Combine 101x and x to get 102x.
102x+80+100z+10y-10x=1000z+100y+8
Subtract 10x from both sides.
92x+80+100z+10y=1000z+100y+8
Combine 102x and -10x to get 92x.
92x+100z+10y=1000z+100y+8-80
Subtract 80 from both sides.
92x+100z+10y=1000z+100y-72
Subtract 80 from 8 to get -72.
92x+10y=1000z+100y-72-100z
Subtract 100z from both sides.
92x+10y=900z+100y-72
Combine 1000z and -100z to get 900z.
92x=900z+100y-72-10y
Subtract 10y from both sides.
92x=900z+90y-72
Combine 100y and -10y to get 90y.
92x=90y+900z-72
The equation is in standard form.
\frac{92x}{92}=\frac{90y+900z-72}{92}
Divide both sides by 92.
x=\frac{90y+900z-72}{92}
Dividing by 92 undoes the multiplication by 92.
x=\frac{45y}{46}+\frac{225z}{23}-\frac{18}{23}
Divide 900z+90y-72 by 92.
101x+80+100z+10y+x=1000z+100y+10x+8
Combine 100x and x to get 101x.
102x+80+100z+10y=1000z+100y+10x+8
Combine 101x and x to get 102x.
102x+80+100z+10y-100y=1000z+10x+8
Subtract 100y from both sides.
102x+80+100z-90y=1000z+10x+8
Combine 10y and -100y to get -90y.
80+100z-90y=1000z+10x+8-102x
Subtract 102x from both sides.
80+100z-90y=1000z-92x+8
Combine 10x and -102x to get -92x.
100z-90y=1000z-92x+8-80
Subtract 80 from both sides.
100z-90y=1000z-92x-72
Subtract 80 from 8 to get -72.
-90y=1000z-92x-72-100z
Subtract 100z from both sides.
-90y=900z-92x-72
Combine 1000z and -100z to get 900z.
-90y=-92x+900z-72
The equation is in standard form.
\frac{-90y}{-90}=\frac{-92x+900z-72}{-90}
Divide both sides by -90.
y=\frac{-92x+900z-72}{-90}
Dividing by -90 undoes the multiplication by -90.
y=\frac{46x}{45}-10z+\frac{4}{5}
Divide 900z-92x-72 by -90.
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{ x } ^ { 2 } - 4 x - 5 = 0
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y = 3x + 4
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Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}