Solve {l}{2.4{(3-x)}-0.6{(2x-3)}=0}{y=x+2.7}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 2.4 {(3 - x)} - 0.6 {(2 x - 3)} = 0 }\\ { y = x + 2.7 }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=5.2$$

Solution Steps

Consider the first equation. Use the distributive property to multiply 2.4 by 3-x.

$$7.2-2.4x-0.6\left(2x-3\right)=0$$

Use the distributive property to multiply -0.6 by 2x-3.

$$7.2-2.4x-1.2x+1.8=0$$

Combine -2.4x and -1.2x to get -3.6x.

$$7.2-3.6x+1.8=0$$

Add 7.2 and 1.8 to get 9.

$$9-3.6x=0$$

Subtract 9 from both sides. Anything subtracted from zero gives its negation.

$$-3.6x=-9$$

Divide both sides by -3.6.

$$x=\frac{-9}{-3.6}$$

Expand \frac{-9}{-3.6} by multiplying both numerator and the denominator by 10.

$$x=\frac{-90}{-36}$$

Reduce the fraction \frac{-90}{-36} to lowest terms by extracting and canceling out -18.

$$x=\frac{5}{2}$$

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

$$y=\frac{5}{2}+2.7$$

Add \frac{5}{2} and 2.7 to get \frac{26}{5}.

$$y=\frac{26}{5}$$

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

$$z=\frac{26}{5}$$

The system is now solved.

$$x=\frac{5}{2} y=\frac{26}{5} z=\frac{26}{5}$$