Solve for u
u=-\frac{5v}{9}+28
Solve for v
v=\frac{252-9u}{5}
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7\left(u-3\right)+5\left(v-4\right)=210-\left(2u-1\right)
Multiply both sides of the equation by 35, the least common multiple of 5,7,35.
7u-21+5\left(v-4\right)=210-\left(2u-1\right)
Use the distributive property to multiply 7 by u-3.
7u-21+5v-20=210-\left(2u-1\right)
Use the distributive property to multiply 5 by v-4.
7u-41+5v=210-\left(2u-1\right)
Subtract 20 from -21 to get -41.
7u-41+5v=210-2u+1
To find the opposite of 2u-1, find the opposite of each term.
7u-41+5v=211-2u
Add 210 and 1 to get 211.
7u-41+5v+2u=211
Add 2u to both sides.
9u-41+5v=211
Combine 7u and 2u to get 9u.
9u+5v=211+41
Add 41 to both sides.
9u+5v=252
Add 211 and 41 to get 252.
9u=252-5v
Subtract 5v from both sides.
\frac{9u}{9}=\frac{252-5v}{9}
Divide both sides by 9.
u=\frac{252-5v}{9}
Dividing by 9 undoes the multiplication by 9.
u=-\frac{5v}{9}+28
Divide 252-5v by 9.
7\left(u-3\right)+5\left(v-4\right)=210-\left(2u-1\right)
Multiply both sides of the equation by 35, the least common multiple of 5,7,35.
7u-21+5\left(v-4\right)=210-\left(2u-1\right)
Use the distributive property to multiply 7 by u-3.
7u-21+5v-20=210-\left(2u-1\right)
Use the distributive property to multiply 5 by v-4.
7u-41+5v=210-\left(2u-1\right)
Subtract 20 from -21 to get -41.
7u-41+5v=210-2u+1
To find the opposite of 2u-1, find the opposite of each term.
7u-41+5v=211-2u
Add 210 and 1 to get 211.
-41+5v=211-2u-7u
Subtract 7u from both sides.
-41+5v=211-9u
Combine -2u and -7u to get -9u.
5v=211-9u+41
Add 41 to both sides.
5v=252-9u
Add 211 and 41 to get 252.
\frac{5v}{5}=\frac{252-9u}{5}
Divide both sides by 5.
v=\frac{252-9u}{5}
Dividing by 5 undoes the multiplication by 5.
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}