Solve {l}{x+5y=2}{0x+ay=1}

$$\left\{ \begin{array} { l } { x + 5 y = 2 } \\ { 0 x + a y = 1 } \end{array} \right.$$

Solve for x, y

$$x=2-\frac{5}{a}$$

$$y=\frac{1}{a}$$

$$a\neq 0$$

Steps Using Substitution

Consider the second equation. Anything times zero gives zero.

$$0+ay=1$$

Anything plus zero gives itself.

$$ay=1$$

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.

$$ay=1,5y+x=2$$

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.

$$ay=1$$

Divide both sides by a.

$$y=\frac{1}{a}$$

Substitute \frac{1}{a} for y in the other equation, 5y+x=2.

$$5\times \frac{1}{a}+x=2$$

Multiply 5 times \frac{1}{a}.

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

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

$$x=2-\frac{5}{a}$$

The system is now solved.

$$y=\frac{1}{a},x=2-\frac{5}{a}$$