Question

1. when 4a - 9b = 22 and b = -2, what is the value of a?

a. $-\frac{10}{3}$
b. 1
c. 4
d. 10

1. what is the solution to the following system of equations?

$f + 3g = 15$
$f - g = 7$

f. -2 5
g. 2 1.5
h. 9 2
j. 18 11

1. if a = 3t - 10 and b = 8 - t, which of the following expresses b in terms of a?

a. $b = \frac{14 - a}{3}$
b. $b = 18 - 3a$
c. $b = 8 - a$
d. $b = 14 - a$

Explanation:

Step1: Substitute $b=-2$ into equation

$4a - 9(-2) = 22$

Step2: Simplify the constant terms

$4a + 18 = 22$

Step3: Isolate the term with $a$

$4a = 22 - 18$
$4a = 4$

Step4: Solve for $a$

$a = \frac{4}{4} = 1$

---

Step1: Subtract the second equation from first

$(f + 3g) - (f - g) = 15 - 7$

Step2: Simplify to solve for $g$

$4g = 8$
$g = \frac{8}{4} = 2$

Step3: Substitute $g=2$ into $f - g = 7$

$f - 2 = 7$

Step4: Solve for $f$

$f = 7 + 2 = 9$

---

Step1: Solve $a=3t-10$ for $t$

$a + 10 = 3t$
$t = \frac{a + 10}{3}$

Step2: Substitute $t$ into $b=8-t$

$b = 8 - \frac{a + 10}{3}$

Step3: Simplify the expression

$b = \frac{24}{3} - \frac{a + 10}{3} = \frac{24 - a - 10}{3} = \frac{14 - a}{3}$

Answer:

1. B. 1
2. H. 9 2
3. A. $b=\frac{14-a}{3}$