Solve {l}{1/4d=8}{3a+1=7}{4(5x-2)=6(2x+7)}

$$\left. \begin{array} { l } { \frac { 1 } { 4 } d = 8 } \\ { 3 a + 1 = 7 } \\ { 4 ( 5 x - 2 ) = 6 ( 2 x + 7 ) } \end{array} \right.$$

Solve for d, a, x

$$x = \frac{25}{4} = 6\frac{1}{4} = 6.25$$

$$d=32$$

$$a=2$$

Solution Steps

Consider the first equation. Multiply both sides by 4, the reciprocal of \frac{1}{4}.

$$d=8\times 4$$

Multiply 8 and 4 to get 32.

$$d=32$$

Consider the second equation. Subtract 1 from both sides.

$$3a=7-1$$

Subtract 1 from 7 to get 6.

$$3a=6$$

Divide both sides by 3.

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

Divide 6 by 3 to get 2.

$$a=2$$

Consider the third equation. Use the distributive property to multiply 4 by 5x-2.

$$20x-8=6\left(2x+7\right)$$

Use the distributive property to multiply 6 by 2x+7.

$$20x-8=12x+42$$

Subtract 12x from both sides.

$$20x-8-12x=42$$

Combine 20x and -12x to get 8x.

$$8x-8=42$$

Add 8 to both sides.

$$8x=42+8$$

Add 42 and 8 to get 50.

$$8x=50$$

Divide both sides by 8.

$$x=\frac{50}{8}$$

Reduce the fraction \frac{50}{8} to lowest terms by extracting and canceling out 2.

$$x=\frac{25}{4}$$

The system is now solved.

$$d=32 a=2 x=\frac{25}{4}$$