Solve for x, y
x=\frac{2k-1}{3}
y=\frac{k+1}{3}
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9x-6k=-3,x+y=k
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.
9x-6k=-3
Pick one of the two equations which is more simple to solve for x by isolating x on the left hand side of the equal sign.
9x=6k-3
Add 6k to both sides of the equation.
x=\frac{2k-1}{3}
Divide both sides by 9.
\frac{2k-1}{3}+y=k
Substitute \frac{-1+2k}{3} for x in the other equation, x+y=k.
y=\frac{k+1}{3}
Subtract \frac{-1+2k}{3} from both sides of the equation.
x=\frac{2k-1}{3},y=\frac{k+1}{3}
The system is now solved.
Examples
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Linear equation
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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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