Solve {l}{5x+2y=12}{4y+5=7}

$$\left. \begin{array} { l } { 5 x + 2 y = 12 } \\ { 4 y + 5 = 7 } \end{array} \right.$$

Solve for x, y

$$x = \frac{11}{5} = 2\frac{1}{5} = 2.2$$

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

Solution Steps

Consider the second equation. Subtract 5 from both sides.

$$4y=7-5$$

Subtract 5 from 7 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.

$$5x+2\times \frac{1}{2}=12$$

Multiply 2 and \frac{1}{2} to get 1.

$$5x+1=12$$

Subtract 1 from both sides.

$$5x=12-1$$

Subtract 1 from 12 to get 11.

$$5x=11$$

Divide both sides by 5.

$$x=\frac{11}{5}$$

The system is now solved.

$$x=\frac{11}{5} y=\frac{1}{2}$$