Solve {l}{4x-15=0}{7x-12y-21=0}

$$\left\{ \begin{array} { l } { 4 x - 15 = 0 } \\ { 7 x - 12 y - 21 = 0 } \end{array} \right.$$

Solve for x, y

$$x = \frac{15}{4} = 3\frac{3}{4} = 3.75$$

$$y=\frac{7}{16}=0.4375$$

Solution Steps

Consider the first equation. Add 15 to both sides. Anything plus zero gives itself.

$$4x=15$$

Divide both sides by 4.

$$x=\frac{15}{4}$$

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

$$7\times \frac{15}{4}-12y-21=0$$

Multiply 7 and \frac{15}{4} to get \frac{105}{4}.

$$\frac{105}{4}-12y-21=0$$

Subtract 21 from \frac{105}{4} to get \frac{21}{4}.

$$\frac{21}{4}-12y=0$$

Subtract \frac{21}{4} from both sides. Anything subtracted from zero gives its negation.

$$-12y=-\frac{21}{4}$$

Divide both sides by -12.

$$y=\frac{-\frac{21}{4}}{-12}$$

Express \frac{-\frac{21}{4}}{-12} as a single fraction.

$$y=\frac{-21}{4\left(-12\right)}$$

Multiply 4 and -12 to get -48.

$$y=\frac{-21}{-48}$$

Reduce the fraction \frac{-21}{-48} to lowest terms by extracting and canceling out -3.

$$y=\frac{7}{16}$$

The system is now solved.

$$x=\frac{15}{4} y=\frac{7}{16}$$