Solve {l}{3x-5y=-9}{4x-9=5}

$$\left. \begin{array} { l } { 3 x - 5 y = - 9 } \\ { 4 x - 9 = 5 } \end{array} \right.$$

Solve for x, y

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

$$y = \frac{39}{10} = 3\frac{9}{10} = 3.9$$

Solution Steps

Consider the second equation. Add 9 to both sides.

$$4x=5+9$$

Add 5 and 9 to get 14.

$$4x=14$$

Divide both sides by 4.

$$x=\frac{14}{4}$$

Reduce the fraction \frac{14}{4} to lowest terms by extracting and canceling out 2.

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

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

$$3\times \frac{7}{2}-5y=-9$$

Multiply 3 and \frac{7}{2} to get \frac{21}{2}.

$$\frac{21}{2}-5y=-9$$

Subtract \frac{21}{2} from both sides.

$$-5y=-9-\frac{21}{2}$$

Subtract \frac{21}{2} from -9 to get -\frac{39}{2}.

$$-5y=-\frac{39}{2}$$

Divide both sides by -5.

$$y=\frac{-\frac{39}{2}}{-5}$$

Express \frac{-\frac{39}{2}}{-5} as a single fraction.

$$y=\frac{-39}{2\left(-5\right)}$$

Multiply 2 and -5 to get -10.

$$y=\frac{-39}{-10}$$

Fraction \frac{-39}{-10} can be simplified to \frac{39}{10} by removing the negative sign from both the numerator and the denominator.

$$y=\frac{39}{10}$$

The system is now solved.

$$x=\frac{7}{2} y=\frac{39}{10}$$