Solve {l}{21-3(x-7)=x+20}{3(t-5)-16t=12-2(t-3)}

$$\left. \begin{array} { l } { 21 - 3 ( x - 7 ) = x + 20 } \\ { 3 ( t - 5 ) - 16 t = 12 - 2 ( t - 3 ) } \end{array} \right.$$

Solve for x, t

$$x = \frac{11}{2} = 5\frac{1}{2} = 5.5$$

$$t=-3$$

Solution Steps

Consider the first equation. Use the distributive property to multiply -3 by x-7.

$$21-3x+21=x+20$$

Add 21 and 21 to get 42.

$$42-3x=x+20$$

Subtract x from both sides.

$$42-3x-x=20$$

Combine -3x and -x to get -4x.

$$42-4x=20$$

Subtract 42 from both sides.

$$-4x=20-42$$

Subtract 42 from 20 to get -22.

$$-4x=-22$$

Divide both sides by -4.

$$x=\frac{-22}{-4}$$

Reduce the fraction \frac{-22}{-4} to lowest terms by extracting and canceling out -2.

$$x=\frac{11}{2}$$

Consider the second equation. Use the distributive property to multiply 3 by t-5.

$$3t-15-16t=12-2\left(t-3\right)$$

Combine 3t and -16t to get -13t.

$$-13t-15=12-2\left(t-3\right)$$

Use the distributive property to multiply -2 by t-3.

$$-13t-15=12-2t+6$$

Add 12 and 6 to get 18.

$$-13t-15=18-2t$$

Add 2t to both sides.

$$-13t-15+2t=18$$

Combine -13t and 2t to get -11t.

$$-11t-15=18$$

Add 15 to both sides.

$$-11t=18+15$$

Add 18 and 15 to get 33.

$$-11t=33$$

Divide both sides by -11.

$$t=\frac{33}{-11}$$

Divide 33 by -11 to get -3.

$$t=-3$$

The system is now solved.

$$x=\frac{11}{2} t=-3$$