Solve for x, y (complex solution)
\left\{\begin{matrix}\\x=\frac{15}{2}=7.5\text{, }y=0\text{, }&\text{unconditionally}\\x=-\frac{15y}{4}+\frac{15}{2}\text{, }y\in \mathrm{C}\text{, }&X=0\end{matrix}\right.
Solve for x, y
\left\{\begin{matrix}\\x=\frac{15}{2}=7.5\text{, }y=0\text{, }&\text{unconditionally}\\x=-\frac{15y}{4}+\frac{15}{2}\text{, }y\in \mathrm{R}\text{, }&X=0\end{matrix}\right.
Graph
Share
Copied to clipboard
2\times 2x+3\left(5y-2\right)=24
Consider the second equation. Multiply both sides of the equation by 6, the least common multiple of 3,2.
4x+3\left(5y-2\right)=24
Multiply 2 and 2 to get 4.
4x+15y-6=24
Use the distributive property to multiply 3 by 5y-2.
4x+15y=24+6
Add 6 to both sides.
4x+15y=30
Add 24 and 6 to get 30.
Xy=0,15y+4x=30
To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.
Xy=0
Pick one of the two equations which is more simple to solve for y by isolating y on the left hand side of the equal sign.
y=0
Divide both sides by X.
4x=30
Substitute 0 for y in the other equation, 15y+4x=30.
x=\frac{15}{2}
Divide both sides by 4.
y=0,x=\frac{15}{2}
The system is now solved.
2\times 2x+3\left(5y-2\right)=24
Consider the second equation. Multiply both sides of the equation by 6, the least common multiple of 3,2.
4x+3\left(5y-2\right)=24
Multiply 2 and 2 to get 4.
4x+15y-6=24
Use the distributive property to multiply 3 by 5y-2.
4x+15y=24+6
Add 6 to both sides.
4x+15y=30
Add 24 and 6 to get 30.
Xy=0,15y+4x=30
To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.
Xy=0
Pick one of the two equations which is more simple to solve for y by isolating y on the left hand side of the equal sign.
y=0
Divide both sides by X.
4x=30
Substitute 0 for y in the other equation, 15y+4x=30.
x=\frac{15}{2}
Divide both sides by 4.
y=0,x=\frac{15}{2}
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}