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
Pie
2 years ago
9

As a first step in solving the system shown, Yumiko multiplies both sides of the equation 2x – 3y = 12 by 6. By what factor shou

ld she multiply both sides of the other equation so that she can add the equations and eliminate a variable? What one-variable equation is she left with after adding?
5x + 6y = 18
2x – 3y = 12

Factor:________
Equation:________x=_________
Mathematics
1 answer:
GenaCL600 [577]2 years ago
7 0

Answer:

Yumiko should multiply the other equation by 3.

If she adds the two equations she would be left with the variable 'x'.

Step-by-step explanation:

Given the two equations are as follows:

$ 2x - 3y = 12 \hspace{5mm} \hdots (1) $

$ 5x + 6y = 18 \hspace{5mm} \hdots (2) $

It is given that she multiplies the first equation by 6. Therefore, (1) becomes

$ 12x - 18y = 72 \hspace{15mm} \hdots (a) $

Now, note that the sign of the variable 'y' is negative. So, if we make the co-effecient of 'y' equal in both the cases, add them it would result in the elimination of the variable 'y'.

The co-effecient of y in Equation (2) is 6. To make it 18 like it is in Equation (1), we multiply throughout by 3.

Therefore, Equation (2) becomes:

$ 15x + 18y = 54 \hspace{5mm} \hdots (b) $

Now, we add Equation (a) and Equation (b).

$ \implies 12x - 18y + 15x + 18y = 72 + 54 $

$ \implies 27x = 126 $

Factor: 3

Equation: 27x = 126

You might be interested in
Can someone please help me asap!
Ahat [919]
Hopes that somehow helps✍︎︎

8 0
3 years ago
Sarah Rhodes prepared one gallon of hot
makvit [3.9K]

1 gallon = 128 ounces

Divide total ounces by ounces per cup:

128 / 4 = 32

She had 32 servings

8 0
2 years ago
The slope of the line below is 1.5. Write the equation of the line in point-slope form, using the coordinates of the labeled poi
Nataly [62]
Point slope form equation: y - y1 = m(x - x1)
in this case

y - 3 = 1.5(x - 4)

Answer
Point slope form equation:
y - 3 = 1.5(x - 4)
5 0
3 years ago
Adam and Brianna plan to install a new tile floor in a classroom. Adam works at a constant rate of 50 tiles per hour, and Briann
natima [27]

Answer:

t≅13.33h

Step-by-step explanation:

Adam (A) works at constant rate of 50tiles/h

Briana (B) works at constant rate of 55tiles/h, this means that A=50 tiles per hour and B=55 tiles per hour, then A+B = 105tiles/h together, but the floor consists of 1400tiles, so if 105 tiles are installed in one hour, then 1400 tiles in how long they will be installed?

t = 1400tiles*h/105tiles≅ 13.33 h

7 0
2 years ago
Find the errors and correct the following mathematical sentences.​
Varvara68 [4.7K]

Answer:

This is your answer ☺️☺️☺️

3 0
3 years ago
Other questions:
  • Do two 2 inch tiles add up to one 4 inch tile?
    12·2 answers
  • A store owner paid 15 dollars for a book. She marked up the price of the book by 40 percent to determine its selling price.
    9·1 answer
  • A coin is slightly bent, and as a result the probability of a head is 0.52. Suppose that you toss the coin four times. Use the B
    14·1 answer
  • Valerie drives 500 meters up a hill that makes an angle of 15degrees with the horizontal. To the nearest tenth of a meter, what
    5·2 answers
  • Solve one variable linear equation 7h-5(3h-8) = -72
    11·2 answers
  • 3(2x+9) = 4+3x-1<br><br> What does x equal
    15·2 answers
  • Do you multiply or divide calories?
    13·1 answer
  • The principle of Park Middle School counted all the students in the seventh grade. She found that the ratio of boys to girls was
    7·1 answer
  • Write the slope-intercept form of the equation for the line given the slope and y-intercept (equation: y=mx+b) Slope = 5, y-inte
    5·1 answer
  • In the coin flipping lab, suppose that you simulated the flipping of a weighted coin 30 times and got 5 heads and 25 tails. What
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!