Solve {c}{-10x+4y=-54}{9x-2x=47}

$$\left. \begin{array} { c } { - 10 x + 4 y = - 54 } \\ { 9 x - 2 x = 47 } \end{array} \right.$$

Solve for x, y

$$x = \frac{47}{7} = 6\frac{5}{7} \approx 6.714285714$$

$$y = \frac{23}{7} = 3\frac{2}{7} \approx 3.285714286$$

Solution Steps

Consider the second equation. Combine 9x and -2x to get 7x.

$$7x=47$$

Divide both sides by 7.

$$x=\frac{47}{7}$$

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

$$-10\times \frac{47}{7}+4y=-54$$

Multiply -10 and \frac{47}{7} to get -\frac{470}{7}.

$$-\frac{470}{7}+4y=-54$$

Add \frac{470}{7} to both sides.

$$4y=-54+\frac{470}{7}$$

Add -54 and \frac{470}{7} to get \frac{92}{7}.

$$4y=\frac{92}{7}$$

Divide both sides by 4.

$$y=\frac{\frac{92}{7}}{4}$$

Express \frac{\frac{92}{7}}{4} as a single fraction.

$$y=\frac{92}{7\times 4}$$

Multiply 7 and 4 to get 28.

$$y=\frac{92}{28}$$

Reduce the fraction \frac{92}{28} to lowest terms by extracting and canceling out 4.

$$y=\frac{23}{7}$$

The system is now solved.

$$x=\frac{47}{7} y=\frac{23}{7}$$