1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
konstantin123 [22]
2 years ago
15

2x + 4y = 15 6x +12y = 45 What would the solution to the system of equations be?

Mathematics
2 answers:
Dimas [21]2 years ago
7 0

Answer:

They both have an infinite number of solutions.

Step-by-step explanation:

Given system of equations:

a) 2x + 4y = 15

b) 6x + 12y = 45

Slope-intercept form: y = mx + b

<u>where:</u>

  • m is the slope
  • b is the y-intercept (when x = 0)

Rewrite <em>both</em> equations into slope-intercept form:

<em>a) 2x + 4y = 15 </em>

⇒ 2x + 4y = 15 [subtract 2x from both sides]

⇒ 2x - 2x + 4y = 15 - 2x

⇒ 4y = - 2x + 15 [divide both sides by 4]

⇒ 4y ÷ 4 = (-2x ÷ 4) + (15 ÷ 4)

\sf \implies y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75

<em>b) 6x + 12y = 45</em>

⇒ 6x + 12y = 45 [subtract 6x from both sides]

⇒ 6x - 6x + 12y = 45 - 6x

⇒ 12y = - 6x + 45 [divide both sides by 12]

⇒ 12y ÷ 12 = (-6x ÷ 12) + (45 ÷ 12)

\sf \implies y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75

New equations:

\sf a)\ y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75\\\\\sf b)\ y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75

Both equations have the same slope (-½), and y-intercept (3.75). Therefore, they both have an infinite number of solutions.

System of equations can have the following:

<u><em>No Solution:</em></u> the same slope (both lines will be parallel)

<u><em>One Solution:</em></u> different slopes and different y-intercepts

<u><em>Infinitely Many Solutions:</em></u> the same slope and y-intercept

Learn more about system of equations here:

brainly.com/question/19575460

brainly.com/question/12198631

solniwko [45]2 years ago
5 0

Looking at the given expression, they do not seem to be in the slope-intercept form which is the most common form used for linear expression. Let us convert the equations that were given in the problem statement to follow the slope-intercept form.

  • Slope-Intercept Form ⇒ y = mx + b
  • m = slope
  • b = y-intercept

Equation #1

<u>Subtract 2x from both sides</u>

  • 2x + 4y = 15
  • 2x - 2x + 4y = 15 - 2x
  • 4y = -2x + 15

<u>Divide both sides by 4</u>

  • \frac{4y}{4} = \frac{-2}{4}x + \frac{15}{4}
  • y = \frac{-2}{4}x + \frac{15}{4}
  • y = -0.5x + 3.75

Equation #2

<u>Subtract 6x from both sides</u>

  • 6x + 12y = 45
  • 6x - 6x + 12y = 45 - 6x
  • 12y = -6x + 45

<u>Divide both sides by 12</u>

  • \frac{12y}{12} = \frac{-6}{12}x + \frac{45}{12}
  • y = \frac{-6}{12}x + \frac{45}{12}
  • y = -0.5x + 3.75

Since both the first and second equation have the same exact number which means that they will fall exactly on top of each other.  Therefore, there are infinite solutions as they will always continue on top of each other.

You might be interested in
What is the ratio 25 to 45 as a simplified fraction​
fenix001 [56]
Reducing the fractions, it is also true that:
Part A = 5/14 of the whole
Part B = 9/14 of the whole
6 0
3 years ago
At Luther's party she made three balloon poodles and two balloon giraffes Which used a total of 17 balloons for Jessica‘s party
olga55 [171]

Answer:

The redaction does not explain the situation.  If we assume that 15 balloons were used to make one ballon poodle and three giraffes, then the answer would be 7,5 balloons for 1 poodle, and 2,5 balloons for a giraffe

Step-by-step explanation:

With 15 balloons we make 1 poodle and 3 giraffes.  This means that 7,5 balloons were used to make 1 poodle, and other 7,5 balloons were used to make 3 giraffes.

If we divide   7,5 balloons between 3, we obtain 2,5.  This means that with 2,5 balloons we make 1 giraffe

4 0
3 years ago
Simplify: 19w5+ (-3075)
AleksAgata [21]
Simplified: 19w^5 - 3075
7 0
3 years ago
HELP ME ASAP, DUE TODAY!!!!!!<br> WILL MARK BRAINIEST
lana [24]

Answer:

Q' = ( 1, 3 )

R' = ( 3, -3)

S' = ( 0, -2)

T' = ( -2, 1 )

4 0
2 years ago
16 more than s is at most −80.
polet [3.4K]

Answer:

s + 16 ≤ −80

Step-by-step explanation:

Analyze each part in the word equation:

"16 more than s"     s increased by 16; s + 16

"is at most"           is equal to or less than; ≤

"−80"               -80

Put the equation back together:

s + 16 ≤ −80

4 0
3 years ago
Other questions:
  • Mr. Baker sells boxes of votive candles to stores. He also has a customer who places a fixed order for designer candles every mo
    10·1 answer
  • Can anyone help me with this and give me steps because I can’t figure it out
    5·1 answer
  • What is the simplified form of 5 - 4y + 2x - 3y - 2 + 5x?
    13·1 answer
  • Jing bought 17 bags of beans. There are b beans in each bag. Write an expression that shows how many beans Jing bought.
    10·2 answers
  • Active time 45:56 please help
    9·2 answers
  • How much would $300 invested at 9% interest compounded continuously be worth after three years.
    14·1 answer
  • Answer correctly for brainliest and also a thanks !
    15·1 answer
  • At a certain time of day, a 1.8-m-tall person standing next to the Washington
    6·1 answer
  • Write an equation of the line that passes through the given point with the given slope
    13·1 answer
  • ASAP timed test pleasssee
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!