Solve {c}{x-4y=10}{3x+6=2}

$$\left. \begin{array} { c } { x - 4 y = 10 } \\ { 3 x + 6 = 2 } \end{array} \right.$$

Solve for x, y

$$x = -\frac{4}{3} = -1\frac{1}{3} \approx -1.333333333$$

$$y = -\frac{17}{6} = -2\frac{5}{6} \approx -2.833333333$$

Solution Steps

Consider the second equation. Subtract 6 from both sides.

$$3x=2-6$$

Subtract 6 from 2 to get -4.

$$3x=-4$$

Divide both sides by 3.

$$x=-\frac{4}{3}$$

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

$$-\frac{4}{3}-4y=10$$

Add \frac{4}{3} to both sides.

$$-4y=10+\frac{4}{3}$$

Add 10 and \frac{4}{3} to get \frac{34}{3}.

$$-4y=\frac{34}{3}$$

Divide both sides by -4.

$$y=\frac{\frac{34}{3}}{-4}$$

Express \frac{\frac{34}{3}}{-4} as a single fraction.

$$y=\frac{34}{3\left(-4\right)}$$

Multiply 3 and -4 to get -12.

$$y=\frac{34}{-12}$$

Reduce the fraction \frac{34}{-12} to lowest terms by extracting and canceling out 2.

$$y=-\frac{17}{6}$$

The system is now solved.

$$x=-\frac{4}{3} y=-\frac{17}{6}$$