Solve {l}{3x-2y=30}{4x+20=7}

$$\left. \begin{array} { l } { 3 x - 2 y = 30 } \\ { 4 x + 20 = 7 } \end{array} \right.$$

Solve for x, y

$$x = -\frac{13}{4} = -3\frac{1}{4} = -3.25$$

$$y = -\frac{159}{8} = -19\frac{7}{8} = -19.875$$

Solution Steps

Consider the second equation. Subtract 20 from both sides.

$$4x=7-20$$

Subtract 20 from 7 to get -13.

$$4x=-13$$

Divide both sides by 4.

$$x=-\frac{13}{4}$$

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

$$3\left(-\frac{13}{4}\right)-2y=30$$

Multiply 3 and -\frac{13}{4} to get -\frac{39}{4}.

$$-\frac{39}{4}-2y=30$$

Add \frac{39}{4} to both sides.

$$-2y=30+\frac{39}{4}$$

Add 30 and \frac{39}{4} to get \frac{159}{4}.

$$-2y=\frac{159}{4}$$

Divide both sides by -2.

$$y=\frac{\frac{159}{4}}{-2}$$

Express \frac{\frac{159}{4}}{-2} as a single fraction.

$$y=\frac{159}{4\left(-2\right)}$$

Multiply 4 and -2 to get -8.

$$y=\frac{159}{-8}$$

Fraction \frac{159}{-8} can be rewritten as -\frac{159}{8} by extracting the negative sign.

$$y=-\frac{159}{8}$$

The system is now solved.

$$x=-\frac{13}{4} y=-\frac{159}{8}$$