Solve {l}{2(a-2)=3(a-5)}{7(x+2)=2(x+2)}

$$\left. \begin{array} { l } { 2 ( a - 2 ) = 3 ( a - 5 ) } \\ { 7 ( x + 2 ) = 2 ( x + 2 ) } \end{array} \right.$$

Solve for a, x

$$x=-2$$

$$a=11$$

Solution Steps

Consider the first equation. Use the distributive property to multiply 2 by a-2.

$$2a-4=3\left(a-5\right)$$

Use the distributive property to multiply 3 by a-5.

$$2a-4=3a-15$$

Subtract 3a from both sides.

$$2a-4-3a=-15$$

Combine 2a and -3a to get -a.

$$-a-4=-15$$

Add 4 to both sides.

$$-a=-15+4$$

Add -15 and 4 to get -11.

$$-a=-11$$

Divide both sides by -1.

$$a=\frac{-11}{-1}$$

Fraction \frac{-11}{-1} can be simplified to 11 by removing the negative sign from both the numerator and the denominator.

$$a=11$$

Consider the second equation. Use the distributive property to multiply 7 by x+2.

$$7x+14=2\left(x+2\right)$$

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

$$7x+14=2x+4$$

Subtract 2x from both sides.

$$7x+14-2x=4$$

Combine 7x and -2x to get 5x.

$$5x+14=4$$

Subtract 14 from both sides.

$$5x=4-14$$

Subtract 14 from 4 to get -10.

$$5x=-10$$

Divide both sides by 5.

$$x=\frac{-10}{5}$$

Divide -10 by 5 to get -2.

$$x=-2$$

The system is now solved.

$$a=11 x=-2$$