Solve {l}{+2x-8=0}{text{ii}2p+2/3=53/4p-1/2}

$$\left. \begin{array} { l } { + 2 x - 8 = 0 } \\ { \text { ii } 2 p + \frac { 2 } { 3 } = 5 \frac { 3 } { 4 } p - \frac { 1 } { 2 } } \end{array} \right.$$

Solve for x, p

$$x=4$$

$$p=\frac{14}{45}\approx 0.311111111$$

Solution Steps

Consider the first equation. Add 8 to both sides. Anything plus zero gives itself.

$$2x=8$$

Divide both sides by 2.

$$x=\frac{8}{2}$$

Divide 8 by 2 to get 4.

$$x=4$$

Consider the second equation. Multiply both sides of the equation by 12, the least common multiple of 3,4,2.

$$24p+8=3\left(5\times 4+3\right)p-6$$

Multiply 5 and 4 to get 20.

$$24p+8=3\left(20+3\right)p-6$$

Add 20 and 3 to get 23.

$$24p+8=3\times 23p-6$$

Multiply 3 and 23 to get 69.

$$24p+8=69p-6$$

Subtract 69p from both sides.

$$24p+8-69p=-6$$

Combine 24p and -69p to get -45p.

$$-45p+8=-6$$

Subtract 8 from both sides.

$$-45p=-6-8$$

Subtract 8 from -6 to get -14.

$$-45p=-14$$

Divide both sides by -45.

$$p=\frac{-14}{-45}$$

Fraction \frac{-14}{-45} can be simplified to \frac{14}{45} by removing the negative sign from both the numerator and the denominator.

$$p=\frac{14}{45}$$

The system is now solved.

$$x=4 p=\frac{14}{45}$$