\left\{ \begin{array} { l } { 2 x + y = 14 } \\ { - \sqrt { 5 } y = 4 \sqrt { 5 } } \end{array} \right.
Solve for x, y
x=9
y=-4
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\left(-\sqrt{5}\right)y=4\sqrt{5},y+2x=14
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.
\left(-\sqrt{5}\right)y=4\sqrt{5}
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=-4
Divide both sides by -\sqrt{5}.
-4+2x=14
Substitute -4 for y in the other equation, y+2x=14.
2x=18
Add 4 to both sides of the equation.
x=9
Divide both sides by 2.
y=-4,x=9
The system is now solved.
Examples
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Linear equation
y = 3x + 4
Arithmetic
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Matrix
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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
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Limits
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