\left( \begin{array} { l l } { x } & { 1 } \end{array} \right) \left( \begin{array} { c c } { 2 } & { - 1 } \\ { - 3 } & { 4 } \end{array} \right) = \left( \begin{array} { l l } { 5 } & { y } \end{array} \right)
Solve for x, y
x=4
y=0
Graph
Share
Copied to clipboard
2x=5+3
Consider the first equation. Add 3 to both sides.
2x=8
Add 5 and 3 to get 8.
x=\frac{8}{2}
Divide both sides by 2.
x=4
Divide 8 by 2 to get 4.
-4+4=y
Consider the second equation. Insert the known values of variables into the equation.
0=y
Add -4 and 4 to get 0.
y=0
Swap sides so that all variable terms are on the left hand side.
x=4 y=0
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}