Solve {l}{3(2p-1)=5-(3p-2)}{0.3(6-x)=0.4(x+8)}

$$\left. \begin{array} { l } { 3 ( 2 p - 1 ) = 5 - ( 3 p - 2 ) } \\ { 0.3 ( 6 - x ) = 0.4 ( x + 8 ) } \end{array} \right.$$

Solve for p, x

$$x=-2$$

$$p = \frac{10}{9} = 1\frac{1}{9} \approx 1.111111111$$

Solution Steps

Consider the first equation. Use the distributive property to multiply 3 by 2p-1.

$$6p-3=5-\left(3p-2\right)$$

To find the opposite of 3p-2, find the opposite of each term.

$$6p-3=5-3p+2$$

Add 5 and 2 to get 7.

$$6p-3=7-3p$$

Add 3p to both sides.

$$6p-3+3p=7$$

Combine 6p and 3p to get 9p.

$$9p-3=7$$

Add 3 to both sides.

$$9p=7+3$$

Add 7 and 3 to get 10.

$$9p=10$$

Divide both sides by 9.

$$p=\frac{10}{9}$$

Consider the second equation. Use the distributive property to multiply 0.3 by 6-x.

$$1.8-0.3x=0.4\left(x+8\right)$$

Use the distributive property to multiply 0.4 by x+8.

$$1.8-0.3x=0.4x+3.2$$

Subtract 0.4x from both sides.

$$1.8-0.3x-0.4x=3.2$$

Combine -0.3x and -0.4x to get -0.7x.

$$1.8-0.7x=3.2$$

Subtract 1.8 from both sides.

$$-0.7x=3.2-1.8$$

Subtract 1.8 from 3.2 to get 1.4.

$$-0.7x=1.4$$

Divide both sides by -0.7.

$$x=\frac{1.4}{-0.7}$$

Expand \frac{1.4}{-0.7} by multiplying both numerator and the denominator by 10.

$$x=\frac{14}{-7}$$

Divide 14 by -7 to get -2.

$$x=-2$$

The system is now solved.

$$p=\frac{10}{9} x=-2$$