Solve {l}{20y+16y=33}{-8x-34y=46}

$$\left\{ \begin{array} { l } { 20 y + 16 y = 33 } \\ { - 8 x - 34 y = 46 } \end{array} \right.$$

Solve for y, x

$$x = -\frac{463}{48} = -9\frac{31}{48} \approx -9.645833333$$

$$y=\frac{11}{12}\approx 0.916666667$$

Solution Steps

Consider the first equation. Combine 20y and 16y to get 36y.

$$36y=33$$

Divide both sides by 36.

$$y=\frac{33}{36}$$

Reduce the fraction \frac{33}{36} to lowest terms by extracting and canceling out 3.

$$y=\frac{11}{12}$$

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

$$-8x-34\times \frac{11}{12}=46$$

Multiply -34 and \frac{11}{12} to get -\frac{187}{6}.

$$-8x-\frac{187}{6}=46$$

Add \frac{187}{6} to both sides.

$$-8x=46+\frac{187}{6}$$

Add 46 and \frac{187}{6} to get \frac{463}{6}.

$$-8x=\frac{463}{6}$$

Divide both sides by -8.

$$x=\frac{\frac{463}{6}}{-8}$$

Express \frac{\frac{463}{6}}{-8} as a single fraction.

$$x=\frac{463}{6\left(-8\right)}$$

Multiply 6 and -8 to get -48.

$$x=\frac{463}{-48}$$

Fraction \frac{463}{-48} can be rewritten as -\frac{463}{48} by extracting the negative sign.

$$x=-\frac{463}{48}$$

The system is now solved.

$$y=\frac{11}{12} x=-\frac{463}{48}$$