Solve {l}{8x+15y=160}{6x=-10+5}

$$\left\{ \begin{array} { l } { 8 x + 15 y = 160 } \\ { 6 x = - 10 + 5 } \end{array} \right.$$

Solve for x, y

$$x=-\frac{5}{6}\approx -0.833333333$$

$$y = \frac{100}{9} = 11\frac{1}{9} \approx 11.111111111$$

Solution Steps

Consider the second equation. Add -10 and 5 to get -5.

$$6x=-5$$

Divide both sides by 6.

$$x=-\frac{5}{6}$$

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

$$8\left(-\frac{5}{6}\right)+15y=160$$

Multiply 8 and -\frac{5}{6} to get -\frac{20}{3}.

$$-\frac{20}{3}+15y=160$$

Add \frac{20}{3} to both sides.

$$15y=160+\frac{20}{3}$$

Add 160 and \frac{20}{3} to get \frac{500}{3}.

$$15y=\frac{500}{3}$$

Divide both sides by 15.

$$y=\frac{\frac{500}{3}}{15}$$

Express \frac{\frac{500}{3}}{15} as a single fraction.

$$y=\frac{500}{3\times 15}$$

Multiply 3 and 15 to get 45.

$$y=\frac{500}{45}$$

Reduce the fraction \frac{500}{45} to lowest terms by extracting and canceling out 5.

$$y=\frac{100}{9}$$

The system is now solved.

$$x=-\frac{5}{6} y=\frac{100}{9}$$