\left\{ \begin{array} { l } { 4 x + 5 y = 20 } \\ { 3 x - 5 y = 15 } \\ { 2 x + 3 y = a } \end{array} \right.
Solve for x, y, a
x=5
y=0
a=10
Graph
Share
Copied to clipboard
x=5-\frac{5}{4}y
Solve 4x+5y=20 for x.
3\left(5-\frac{5}{4}y\right)-5y=15 2\left(5-\frac{5}{4}y\right)+3y=a
Substitute 5-\frac{5}{4}y for x in the second and third equation.
y=0 a=10+\frac{1}{2}y
Solve these equations for y and a respectively.
a=10+\frac{1}{2}\times 0
Substitute 0 for y in the equation a=10+\frac{1}{2}y.
a=10
Calculate a from a=10+\frac{1}{2}\times 0.
x=5-\frac{5}{4}\times 0
Substitute 0 for y in the equation x=5-\frac{5}{4}y.
x=5
Calculate x from x=5-\frac{5}{4}\times 0.
x=5 y=0 a=10
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}