Solve {l}{2b+7=8b-3}{8y-9=5y+6}

$$\left. \begin{array} { l } { 2 b + 7 = 8 b - 3 } \\ { 8 y - 9 = 5 y + 6 } \end{array} \right.$$

Solve for b, y

$$y=5$$

$$b = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$$

Solution Steps

Consider the first equation. Subtract 8b from both sides.

$$2b+7-8b=-3$$

Combine 2b and -8b to get -6b.

$$-6b+7=-3$$

Subtract 7 from both sides.

$$-6b=-3-7$$

Subtract 7 from -3 to get -10.

$$-6b=-10$$

Divide both sides by -6.

$$b=\frac{-10}{-6}$$

Reduce the fraction \frac{-10}{-6} to lowest terms by extracting and canceling out -2.

$$b=\frac{5}{3}$$

Consider the second equation. Subtract 5y from both sides.

$$8y-9-5y=6$$

Combine 8y and -5y to get 3y.

$$3y-9=6$$

Add 9 to both sides.

$$3y=6+9$$

Add 6 and 9 to get 15.

$$3y=15$$

Divide both sides by 3.

$$y=\frac{15}{3}$$

Divide 15 by 3 to get 5.

$$y=5$$

The system is now solved.

$$b=\frac{5}{3} y=5$$