Solve {l}{6x+8=7}{7x+2y=8}

$$\left\{ \begin{array} { l } { 6 x + 8 = 7 } \\ { 7 x + 2 y = 8 } \end{array} \right.$$

Solve for x, y

$$x=-\frac{1}{6}\approx -0.166666667$$

$$y = \frac{55}{12} = 4\frac{7}{12} \approx 4.583333333$$

Solution Steps

Consider the first equation. Subtract 8 from both sides.

$$6x=7-8$$

Subtract 8 from 7 to get -1.

$$6x=-1$$

Divide both sides by 6.

$$x=-\frac{1}{6}$$

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

$$7\left(-\frac{1}{6}\right)+2y=8$$

Multiply 7 and -\frac{1}{6} to get -\frac{7}{6}.

$$-\frac{7}{6}+2y=8$$

Add \frac{7}{6} to both sides.

$$2y=8+\frac{7}{6}$$

Add 8 and \frac{7}{6} to get \frac{55}{6}.

$$2y=\frac{55}{6}$$

Divide both sides by 2.

$$y=\frac{\frac{55}{6}}{2}$$

Express \frac{\frac{55}{6}}{2} as a single fraction.

$$y=\frac{55}{6\times 2}$$

Multiply 6 and 2 to get 12.

$$y=\frac{55}{12}$$

The system is now solved.

$$x=-\frac{1}{6} y=\frac{55}{12}$$