Ask question

Ask question

All categories

3 years ago

13

What value of b will cause the system to have an infinite

1 answer:

kvasek [131]3 years ago

8 0

Hi there!

The way that an infinite number of solutions is achieved is when the two equations, when solved together, get an answer which is just a number equal to the same number. To do this, first substitute 6x-b in for y in the second equation.

$-3x+\frac{1}{2}(6x-b)=-3$

$-3x+3x-\frac{1}{2}b=-3$

$-\frac{1}{2}b=-3$

Now, we see that b needs to be equal to -3 when multiplied by -1/2. When both sides are divided by -1/2, b becomes equal to 6. Thus, b must be 6.

Check work:

$6x-6=y$

$-3x+\frac{1}{2}(6x-6)=-3$

$-3x+3x-3=-3$

$-3=-3$

Thus, as they are equal to each other, the answer is correct. b = 6.

Hope this helps!

You might be interested in

Could someone help me arrange these pairs of points in increasing order of the slopes of the lines joining them. (15, 30) and (2

Zina [86]

Answer:

(e) (27, 2) and (243, 18)

(g) (63, 9) and (84, 12)

(d) (45, 15) and (60, 20)

(c) (27, 12) and (72, 32)

(a) (15, 30) and (20, 40)

(b) (12, 32) and (18, 48)

(f) (18, 63) and (24, 84)

Step-by-step explanation:

Required

Arrange in increasing order of slope

Slope (m) is calculated using:

$m = \frac{y_2 -y_1}{x_2 - x_1}$

So, we have:

(a) (15, 30) and (20, 40)

$m = \frac{40 -30}{20- 15}$

$m = \frac{10}{5}$

$m =2.00$

(b) (12, 32) and (18, 48)

$m = \frac{48 -32}{18- 12}$

$m = \frac{16}{6}$

$m = 2.67$

(c) (27, 12) and (72, 32)

$m = \frac{32-12}{72- 27}$

$m = \frac{20}{45}$

$m = 0.44$

(d) (45, 15) and (60, 20)

$m = \frac{20-15}{60- 45}$

$m = \frac{5}{15}$

$m = 0.33$

(e) (27, 2) and (243, 18)

$m = \frac{18-2}{243- 27}$

$m = \frac{16}{216}$

$m = 0.07$

(f) (18, 63) and (24, 84)

$m = \frac{84-63}{24- 18}$

$m = \frac{21}{6}$

$m = 3.50$

(g) (63, 9) and (84, 12)

$m = \frac{12 -9}{84- 63}$

$m = \frac{3}{21}$

$m = 0.14$

From least to greatest slope, the pair of points are:

(e) (27, 2) and (243, 18)

(g) (63, 9) and (84, 12)

(d) (45, 15) and (60, 20)

(c) (27, 12) and (72, 32)

(a) (15, 30) and (20, 40)

(b) (12, 32) and (18, 48)

(f) (18, 63) and (24, 84)

6 0

3 years ago

Rita earns $10 per hour. She puts 5% of her earnings in savings. Write inequality to find how many hours Rita must work to save

Rina8888 [55]

Answer:

Rita must work 50 days to save at least $25.

Step-by-step explanation:

The amount Rita earns per hour = $10

The saving percentage = 5%

So, the savings of Rita per hour = 5% of $10

⇒5% of $10 = $\frac{5}{100} \times 10 = 0.5$

or Rita saves $0.5 per hour.

The amount she wants to save at minimum = $25

So, let she works at the minimum of k Days.

⇒ $\textrm{The number of hours she has to work} = \frac{\textrm{Amount she needs saving}}{\textrm{Amount saved in 1 hour}}$

or, $k = \frac{25}{0.5} = 50$

The number of hours she has to work = 50 days

Hence, Rita must work 50 days to save at least $25.

3 0

3 years ago

Is 1\8 equivalent to 4\32

Klio2033 [76]

Yes it is, 8•3 is 32

4 0

3 years ago

4. Solve the equation for the given variable. For each step. Identity the property used to convert the equation. 22x + 11 = 4x -

Andrei [34K]

Answer:

x=-1

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Which graph shows the line y = -3x + 1

Nikolay [14]

Line B

Explanation:

The slope is negative so the line is going to the left. The y-intersect is 1.

7 0

3 years ago

Read 2 more answers