Question

1. $6r - 6t = 6$ $3r - 6t = 15$

Explanation:

Step1: Label the two equations

Let:
$$6r - 6t = 6 \tag{1}$$
$$3r - 6t = 15 \tag{2}$$

Step2: Subtract equation (2) from (1)

Eliminate $-6t$ by subtraction:
$$(6r - 6t) - (3r - 6t) = 6 - 15$$
$$6r - 6t - 3r + 6t = -9$$
$$3r = -9$$

Step3: Solve for $r$

Divide both sides by 3:
$$r = \frac{-9}{3} = -3$$

Step4: Substitute $r=-3$ into (1)

Find the value of $t$:
$$6(-3) - 6t = 6$$
$$-18 - 6t = 6$$

Step5: Solve for $t$

Isolate the term with $t$:
$$-6t = 6 + 18$$
$$-6t = 24$$
$$t = \frac{24}{-6} = -4$$

Answer:

$r=-3$, $t=-4$