Solve {l}{5x+3a=15}{2y=4x+15}{1y-17a=14}

$$\left. \begin{array} { l } { 5 x + 3 a = 15 } \\ { 2 y = 4 x + 15 } \\ { 1 y - 17 a = 14 } \end{array} \right.$$

Solve for x, a, y

$$x = \frac{549}{182} = 3\frac{3}{182} \approx 3.016483516$$

$$y = \frac{2463}{182} = 13\frac{97}{182} \approx 13.532967033$$

$$a=-\frac{5}{182}\approx -0.027472527$$

Short Steps Using Substitution

Solve 5x+3a=15 for x.

$$x=3-\frac{3}{5}a$$

Substitute 3-\frac{3}{5}a for x in the equation 2y=4x+15.

$$2y=4\left(3-\frac{3}{5}a\right)+15$$

Solve the second equation for a and the third equation for y.

$$a=\frac{45}{4}-\frac{5}{6}y y=17a+14$$

Substitute \frac{45}{4}-\frac{5}{6}y for a in the equation y=17a+14.

$$y=17\left(\frac{45}{4}-\frac{5}{6}y\right)+14$$

Solve y=17\left(\frac{45}{4}-\frac{5}{6}y\right)+14 for y.

$$y=\frac{2463}{182}$$

Substitute \frac{2463}{182} for y in the equation a=\frac{45}{4}-\frac{5}{6}y.

$$a=\frac{45}{4}-\frac{5}{6}\times \frac{2463}{182}$$

Calculate a from a=\frac{45}{4}-\frac{5}{6}\times \frac{2463}{182}.

$$a=-\frac{5}{182}$$

Substitute -\frac{5}{182} for a in the equation x=3-\frac{3}{5}a.

$$x=3-\frac{3}{5}\left(-\frac{5}{182}\right)$$

Calculate x from x=3-\frac{3}{5}\left(-\frac{5}{182}\right).

$$x=\frac{549}{182}$$

The system is now solved.

$$x=\frac{549}{182} a=-\frac{5}{182} y=\frac{2463}{182}$$