Solve {l}{4x-10-10a-3=0}{10-2x+10a+y=0}

$$\left\{ \begin{array} { l } { 4 x - 10 - 10 a - 3 = 0 } \\ { 10 - 2 x + 10 a + y = 0 } \end{array} \right.$$

Solve for x, y

$$x=\frac{5a}{2}+\frac{13}{4}$$

$$y=-5a-\frac{7}{2}$$

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.

$$4x-10a-13=0,-2x+y+10a+10=0$$

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.

$$4x-10a-13=0$$

Subtract -13-10a from both sides of the equation.

$$4x=10a+13$$

Divide both sides by 4.

$$x=\frac{5a}{2}+\frac{13}{4}$$

Substitute \frac{13}{4}+\frac{5a}{2} for x in the other equation, -2x+y+10a+10=0.

$$-2\left(\frac{5a}{2}+\frac{13}{4}\right)+y+10a+10=0$$

Multiply -2 times \frac{13}{4}+\frac{5a}{2}.

$$-5a-\frac{13}{2}+y+10a+10=0$$

Add -\frac{13}{2}-5a to 10+10a.

$$y+5a+\frac{7}{2}=0$$

Subtract \frac{7}{2}+5a from both sides of the equation.

$$y=-5a-\frac{7}{2}$$

The system is now solved.

$$x=\frac{5a}{2}+\frac{13}{4},y=-5a-\frac{7}{2}$$