Solve {l}{3x+y=7}{4y+1=6}

$$\left. \begin{array} { l } { 3 x + y = 7 } \\ { 4 y + 1 = 6 } \end{array} \right.$$

Solve for x, y

$$x = \frac{23}{12} = 1\frac{11}{12} \approx 1.916666667$$

$$y = \frac{5}{4} = 1\frac{1}{4} = 1.25$$

Solution Steps

Consider the second equation. Subtract 1 from both sides.

$$4y=6-1$$

Subtract 1 from 6 to get 5.

$$4y=5$$

Divide both sides by 4.

$$y=\frac{5}{4}$$

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

$$3x+\frac{5}{4}=7$$

Subtract \frac{5}{4} from both sides.

$$3x=7-\frac{5}{4}$$

Subtract \frac{5}{4} from 7 to get \frac{23}{4}.

$$3x=\frac{23}{4}$$

Divide both sides by 3.

$$x=\frac{\frac{23}{4}}{3}$$

Express \frac{\frac{23}{4}}{3} as a single fraction.

$$x=\frac{23}{4\times 3}$$

Multiply 4 and 3 to get 12.

$$x=\frac{23}{12}$$

The system is now solved.

$$x=\frac{23}{12} y=\frac{5}{4}$$