Solve {l}{3x+5y=7}{7x+7=8}

$$\left. \begin{array} { l } { 3 x + 5 y = 7 } \\ { 7 x + 7 = 8 } \end{array} \right.$$

Solve for x, y

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

$$y = \frac{46}{35} = 1\frac{11}{35} \approx 1.314285714$$

Solution Steps

Consider the second equation. Subtract 7 from both sides.

$$7x=8-7$$

Subtract 7 from 8 to get 1.

$$7x=1$$

Divide both sides by 7.

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

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

$$3\times \frac{1}{7}+5y=7$$

Multiply 3 and \frac{1}{7} to get \frac{3}{7}.

$$\frac{3}{7}+5y=7$$

Subtract \frac{3}{7} from both sides.

$$5y=7-\frac{3}{7}$$

Subtract \frac{3}{7} from 7 to get \frac{46}{7}.

$$5y=\frac{46}{7}$$

Divide both sides by 5.

$$y=\frac{\frac{46}{7}}{5}$$

Express \frac{\frac{46}{7}}{5} as a single fraction.

$$y=\frac{46}{7\times 5}$$

Multiply 7 and 5 to get 35.

$$y=\frac{46}{35}$$

The system is now solved.

$$x=\frac{1}{7} y=\frac{46}{35}$$