Solve {l}{3x-1y=5}{4y+2=4}

$$\left. \begin{array} { l } { 3 x - 1 y = 5 } \\ { 4 y + 2 = 4 } \end{array} \right.$$

Solve for x, y

$$x = \frac{11}{6} = 1\frac{5}{6} \approx 1.833333333$$

$$y=\frac{1}{2}=0.5$$

Solution Steps

Consider the second equation. Subtract 2 from both sides.

$$4y=4-2$$

Subtract 2 from 4 to get 2.

$$4y=2$$

Divide both sides by 4.

$$y=\frac{2}{4}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$y=\frac{1}{2}$$

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

$$3x-\frac{1}{2}=5$$

Add \frac{1}{2} to both sides.

$$3x=5+\frac{1}{2}$$

Add 5 and \frac{1}{2} to get \frac{11}{2}.

$$3x=\frac{11}{2}$$

Divide both sides by 3.

$$x=\frac{\frac{11}{2}}{3}$$

Express \frac{\frac{11}{2}}{3} as a single fraction.

$$x=\frac{11}{2\times 3}$$

Multiply 2 and 3 to get 6.

$$x=\frac{11}{6}$$

The system is now solved.

$$x=\frac{11}{6} y=\frac{1}{2}$$