Solve for x, y
x=\frac{b-a}{2}
y=\frac{c}{4}+\frac{7a}{8}-\frac{7b}{8}
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2x=b-a
Consider the first equation. Subtract a from both sides.
7x+4y=c
Consider the second equation. Swap sides so that all variable terms are on the left hand side.
2x=b-a,7x+4y=c
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.
2x=b-a
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.
x=\frac{b-a}{2}
Divide both sides by 2.
7\times \frac{b-a}{2}+4y=c
Substitute \frac{b-a}{2} for x in the other equation, 7x+4y=c.
\frac{7b-7a}{2}+4y=c
Multiply 7 times \frac{b-a}{2}.
4y=\frac{7a}{2}-\frac{7b}{2}+c
Subtract \frac{7b-7a}{2} from both sides of the equation.
y=\frac{c}{4}+\frac{7a}{8}-\frac{7b}{8}
Divide both sides by 4.
x=\frac{b-a}{2},y=\frac{c}{4}+\frac{7a}{8}-\frac{7b}{8}
The system is now solved.
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}