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

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

Solve for x, y

$$x=2$$

$$y=\frac{2}{3}\approx 0.666666667$$

Solution Steps

Consider the second equation. Combine x and 2x to get 3x.

$$3x=6$$

Divide both sides by 3.

$$x=\frac{6}{3}$$

Divide 6 by 3 to get 2.

$$x=2$$

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

$$4\times 2=10-3y$$

Multiply 4 and 2 to get 8.

$$8=10-3y$$

Swap sides so that all variable terms are on the left hand side.

$$10-3y=8$$

Subtract 10 from both sides.

$$-3y=8-10$$

Subtract 10 from 8 to get -2.

$$-3y=-2$$

Divide both sides by -3.

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

Fraction \frac{-2}{-3} can be simplified to \frac{2}{3} by removing the negative sign from both the numerator and the denominator.

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

The system is now solved.

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