Solve for x, y, z
z=56
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2\left(2x-1\right)-5\left(x-2\right)=0
Consider the first equation. Multiply both sides of the equation by 10, the least common multiple of 5,2.
4x-2-5\left(x-2\right)=0
Use the distributive property to multiply 2 by 2x-1.
4x-2-5x+10=0
Use the distributive property to multiply -5 by x-2.
-x-2+10=0
Combine 4x and -5x to get -x.
-x+8=0
Add -2 and 10 to get 8.
-x=-8
Subtract 8 from both sides. Anything subtracted from zero gives its negation.
x=\frac{-8}{-1}
Divide both sides by -1.
x=8
Fraction \frac{-8}{-1} can be simplified to 8 by removing the negative sign from both the numerator and the denominator.
y=7\times 8
Consider the second equation. Insert the known values of variables into the equation.
y=56
Multiply 7 and 8 to get 56.
z=56
Consider the third equation. Insert the known values of variables into the equation.
x=8 y=56 z=56
The system is now solved.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
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}