Solve {c}{5x+3y=9}{10x+17=-18}

$$\left. \begin{array} { c } { 5 x + 3 y = 9 } \\ { 10 x + 17 = - 18 } \end{array} \right.$$

Solve for x, y

$$x = -\frac{7}{2} = -3\frac{1}{2} = -3.5$$

$$y = \frac{53}{6} = 8\frac{5}{6} \approx 8.833333333$$

Solution Steps

Consider the second equation. Subtract 17 from both sides.

$$10x=-18-17$$

Subtract 17 from -18 to get -35.

$$10x=-35$$

Divide both sides by 10.

$$x=\frac{-35}{10}$$

Reduce the fraction \frac{-35}{10} to lowest terms by extracting and canceling out 5.

$$x=-\frac{7}{2}$$

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

$$5\left(-\frac{7}{2}\right)+3y=9$$

Multiply 5 and -\frac{7}{2} to get -\frac{35}{2}.

$$-\frac{35}{2}+3y=9$$

Add \frac{35}{2} to both sides.

$$3y=9+\frac{35}{2}$$

Add 9 and \frac{35}{2} to get \frac{53}{2}.

$$3y=\frac{53}{2}$$

Divide both sides by 3.

$$y=\frac{\frac{53}{2}}{3}$$

Express \frac{\frac{53}{2}}{3} as a single fraction.

$$y=\frac{53}{2\times 3}$$

Multiply 2 and 3 to get 6.

$$y=\frac{53}{6}$$

The system is now solved.

$$x=-\frac{7}{2} y=\frac{53}{6}$$