Solve {c}{k-1/2y=5/4}{x+y=2}

$$\left\{ \begin{array} { c } { k - \frac { 1 } { 2 } y = \frac { 5 } { 4 } } \\ { x + y = 2 } \end{array} \right.$$

Solve for x, y

$$x=\frac{9}{2}-2k$$

$$y=2k-\frac{5}{2}$$

Steps Using Substitution

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.

$$-\frac{1}{2}y+k=\frac{5}{4},y+x=2$$

Pick one of the two equations which is more simple to solve for y by isolating y on the left hand side of the equal sign.

$$-\frac{1}{2}y+k=\frac{5}{4}$$

Subtract k from both sides of the equation.

$$-\frac{1}{2}y=\frac{5}{4}-k$$

Multiply both sides by -2.

$$y=2k-\frac{5}{2}$$

Substitute -\frac{5}{2}+2k for y in the other equation, y+x=2.

$$2k-\frac{5}{2}+x=2$$

Subtract -\frac{5}{2}+2k from both sides of the equation.

$$x=\frac{9}{2}-2k$$

The system is now solved.

$$y=2k-\frac{5}{2},x=\frac{9}{2}-2k$$