Solve {l}{7y=1}{ay+(a-1)y=3}

$$\left\{ \begin{array} { l } { 7 y = 1 } \\ { a y + ( a - 1 ) y = 3 } \end{array} \right.$$

Solve for y, a

$$y=\frac{1}{7}\approx 0.142857143$$

$$a=11$$

Solution Steps

Consider the first equation. Divide both sides by 7.

$$y=\frac{1}{7}$$

Consider the second equation. Insert the known values of variables into the equation.

$$a\times \frac{1}{7}+\left(a-1\right)\times \frac{1}{7}=3$$

Use the distributive property to multiply a-1 by \frac{1}{7}.

$$a\times \frac{1}{7}+\frac{1}{7}a-\frac{1}{7}=3$$

Combine a\times \frac{1}{7} and \frac{1}{7}a to get \frac{2}{7}a.

$$\frac{2}{7}a-\frac{1}{7}=3$$

Add \frac{1}{7} to both sides.

$$\frac{2}{7}a=3+\frac{1}{7}$$

Add 3 and \frac{1}{7} to get \frac{22}{7}.

$$\frac{2}{7}a=\frac{22}{7}$$

Multiply both sides by \frac{7}{2}, the reciprocal of \frac{2}{7}.

$$a=\frac{22}{7}\times \frac{7}{2}$$

Multiply \frac{22}{7} and \frac{7}{2} to get 11.

$$a=11$$

The system is now solved.

$$y=\frac{1}{7} a=11$$