Solve {l}{52x+3=7}{78-2y=7}

$$\left. \begin{array} { l } { 52 x + 3 = 7 } \\ { 78 - 2 y = 7 } \end{array} \right.$$

Solve for x, y

$$x=\frac{1}{13}\approx 0.076923077$$

$$y = \frac{71}{2} = 35\frac{1}{2} = 35.5$$

Solution Steps

Consider the first equation. Subtract 3 from both sides.

$$52x=7-3$$

Subtract 3 from 7 to get 4.

$$52x=4$$

Divide both sides by 52.

$$x=\frac{4}{52}$$

Reduce the fraction \frac{4}{52} to lowest terms by extracting and canceling out 4.

$$x=\frac{1}{13}$$

Consider the second equation. Subtract 78 from both sides.

$$-2y=7-78$$

Subtract 78 from 7 to get -71.

$$-2y=-71$$

Divide both sides by -2.

$$y=\frac{-71}{-2}$$

Fraction \frac{-71}{-2} can be simplified to \frac{71}{2} by removing the negative sign from both the numerator and the denominator.

$$y=\frac{71}{2}$$

The system is now solved.

$$x=\frac{1}{13} y=\frac{71}{2}$$