\left\{ \begin{array} { c } { - ( 3 x - 2 ) = y - 2 } \\ { - ( 2 x + y ) = 2 ( y - x ) - 3 } \end{array} \right.
Solve for x, y
x=1
y=1
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-3x+2=y-2
Consider the first equation. To find the opposite of 3x-2, find the opposite of each term.
-3x+2-y=-2
Subtract y from both sides.
-3x-y=-2-2
Subtract 2 from both sides.
-3x-y=-4
Subtract 2 from -2 to get -4.
-2x-y=2\left(y-x\right)-3
Consider the second equation. To find the opposite of 2x+y, find the opposite of each term.
-2x-y=2y-2x-3
Use the distributive property to multiply 2 by y-x.
-2x-y-2y=-2x-3
Subtract 2y from both sides.
-2x-3y=-2x-3
Combine -y and -2y to get -3y.
-2x-3y+2x=-3
Add 2x to both sides.
-3y=-3
Combine -2x and 2x to get 0.
y=\frac{-3}{-3}
Divide both sides by -3.
y=1
Divide -3 by -3 to get 1.
-3x-1=-4
Consider the first equation. Insert the known values of variables into the equation.
-3x=-4+1
Add 1 to both sides.
-3x=-3
Add -4 and 1 to get -3.
x=\frac{-3}{-3}
Divide both sides by -3.
x=1
Divide -3 by -3 to get 1.
x=1 y=1
The system is now solved.
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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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