Solve for u
u=\frac{7+4v+y-x}{2}
Solve for v
v=\frac{x-y+2u-7}{4}
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2u-4v-7+x=y
Subtract 4 from -3 to get -7.
2u-7+x=y+4v
Add 4v to both sides.
2u+x=y+4v+7
Add 7 to both sides.
2u=y+4v+7-x
Subtract x from both sides.
2u=7+4v+y-x
The equation is in standard form.
\frac{2u}{2}=\frac{7+4v+y-x}{2}
Divide both sides by 2.
u=\frac{7+4v+y-x}{2}
Dividing by 2 undoes the multiplication by 2.
u=\frac{y}{2}-\frac{x}{2}+2v+\frac{7}{2}
Divide y+4v+7-x by 2.
2u-4v-7+x=y
Subtract 4 from -3 to get -7.
-4v-7+x=y-2u
Subtract 2u from both sides.
-4v+x=y-2u+7
Add 7 to both sides.
-4v=y-2u+7-x
Subtract x from both sides.
-4v=7-2u+y-x
The equation is in standard form.
\frac{-4v}{-4}=\frac{7-2u+y-x}{-4}
Divide both sides by -4.
v=\frac{7-2u+y-x}{-4}
Dividing by -4 undoes the multiplication by -4.
v=\frac{u}{2}+\frac{x}{4}-\frac{y}{4}-\frac{7}{4}
Divide y-2u+7-x by -4.
Examples
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{ 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}