Question

1. $y = -4x + 3$

$y = 2\frac{1}{2}x - 1$

a. $(0.308, 1.769)$

b. $(0.615, 0.538)$

c. $(0.615, -1.462)$

d. $(-1.333, 2.333)$

1. tom has a collection of 30 cds and nita has a collection of 18 cds. tom is adding 1 cd a month to his collection while nita is adding 5 cds a month to her collection. find the number of months after which they will have the same number of cds.

a. 1 month

b. 3 months

c. 2 months

d. 33 months

what is the solution of the system? use substitution.

1. $x - y = -6$

$6x - 3y = -9$

a. $(1, 7)$

b. $(3, 9)$

c. $\left(-6, \frac{3}{2}\
ight)$

d. $(4, -11)$

Explanation:

Question 25

Step1: Set equations equal

Since \( y = -4x + 3 \) and \( y = 2\frac{1}{2}x - 1 \), substitute \( y \):
\( -4x + 3 = \frac{5}{2}x - 1 \)

Step2: Solve for \( x \)

Multiply by 2: \( -8x + 6 = 5x - 2 \)
\( -8x - 5x = -2 - 6 \)
\( -13x = -8 \)
\( x = \frac{8}{13} \approx 0.615 \)

Step3: Find \( y \)

Substitute \( x \) into \( y = -4x + 3 \):
\( y = -4(\frac{8}{13}) + 3 = -\frac{32}{13} + \frac{39}{13} = \frac{7}{13} \approx 0.538 \)

Step1: Define variables

Let \( m \) = months. Tom’s CDs: \( 30 + m \), Nita’s CDs: \( 18 + 5m \).

Step2: Set equal

\( 30 + m = 18 + 5m \)

Step3: Solve for \( m \)

\( 30 - 18 = 5m - m \)
\( 12 = 4m \)
\( m = 3 \)

Step1: Solve \( x - y = -6 \) for \( x \)

\( x = y - 6 \)

Step2: Substitute into \( 6x - 3y = -9 \)

\( 6(y - 6) - 3y = -9 \)
\( 6y - 36 - 3y = -9 \)
\( 3y = 27 \)
\( y = 9 \)

Step3: Find \( x \)

\( x = 9 - 6 = 3 \)

Answer:

b. \( (0.615, 0.538) \)

Question 26