\left\{ \begin{array} { l } { \frac { x } { 2 } - \frac { x - 2 } { 3 } = 2 } \\ { 3 x + 2 y = 16 } \end{array} \right.
Solve for x, y
x=8
y=-4
Graph
Share
Copied to clipboard
3x-2\left(x-2\right)=12
Consider the first equation. Multiply both sides of the equation by 6, the least common multiple of 2,3.
3x-2x+4=12
Use the distributive property to multiply -2 by x-2.
x+4=12
Combine 3x and -2x to get x.
x=12-4
Subtract 4 from both sides.
x=8
Subtract 4 from 12 to get 8.
3\times 8+2y=16
Consider the second equation. Insert the known values of variables into the equation.
24+2y=16
Multiply 3 and 8 to get 24.
2y=16-24
Subtract 24 from both sides.
2y=-8
Subtract 24 from 16 to get -8.
y=\frac{-8}{2}
Divide both sides by 2.
y=-4
Divide -8 by 2 to get -4.
x=8 y=-4
The system is now solved.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
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}