Solve {l}{2x+3y=19}{4x+11=53}

$$\left. \begin{array} { l } { 2 x + 3 y = 19 } \\ { 4 x + 11 = 53 } \end{array} \right.$$

Solve for x, y

$$x = \frac{21}{2} = 10\frac{1}{2} = 10.5$$

$$y=-\frac{2}{3}\approx -0.666666667$$

Solution Steps

Consider the second equation. Subtract 11 from both sides.

$$4x=53-11$$

Subtract 11 from 53 to get 42.

$$4x=42$$

Divide both sides by 4.

$$x=\frac{42}{4}$$

Reduce the fraction \frac{42}{4} to lowest terms by extracting and canceling out 2.

$$x=\frac{21}{2}$$

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

$$2\times \frac{21}{2}+3y=19$$

Multiply 2 and \frac{21}{2} to get 21.

$$21+3y=19$$

Subtract 21 from both sides.

$$3y=19-21$$

Subtract 21 from 19 to get -2.

$$3y=-2$$

Divide both sides by 3.

$$y=-\frac{2}{3}$$

The system is now solved.

$$x=\frac{21}{2} y=-\frac{2}{3}$$