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
kkurt [141]
3 years ago
15

Can someone help me please? Use the linear combination method to solve the system of equations. Pretty please show your work and

what do you know about the two lines in this system of equations? I struggle a lot when it comes to these x-3y=13 2x+4y=-4

Mathematics
2 answers:
Pavel [41]3 years ago
5 0

Answer:

  (x, y) = (4, -3)

Step-by-step explanation:

  • x-3y=13
  • 2x+4y=-4

First of all, look at the given equations. Here, we see that the second equation has coefficients that all have a factor of 2. If we divide that out, we get an equation that has an x-coefficient of 1, matching the x-coefficient in the first equation.

Here is the reduced second equation:

  x +2y = -2

Now, if we subtract one equation from the other, the variable x will be eliminated. We want to choose that subtraction wisely.

We note that the y-coefficient in the first equation is less than that in the second equation. If we subtract the first equation from the second, the result will have a positive y-coefficient:

  (x +2y) -(x -3y) = (-2) -(13)

  5y = -15 . . . . . . . . . . . . . . . . simplify. Note that the x-variable is eliminated, which is the purpose of this exercise.

  y = -3 . . . . . . . divide by 5

We can use this value in the reduced second equation to find the value of x:

  x +2(-3) = -2

  x = 4 . . . . . . . . . add 6 and simplify

The solution is (x, y) = (4, -3).

_____

I find a graphing calculator provides an easy and reliable check of the answer.

_____

<em>Comment on linear combination</em>

This method is often called "elimination," because the purpose of combining the equations in a particular way is to eliminate one of the variables. This requires you look at the coefficients of the variables and devise a plan to combine them so the resulting coefficient for one of the variables is zero.

In the worst case, you can combine ...

  • ax +by = c
  • dx +ey = f

by multiplying the second equation by <em>a</em> and the first by <em>-d</em>:

  a(dx +ey) -d(ax +by) = a( f) -d(c)

  y(ae -bd) = fa -cd . . . . . . simplify; x is eliminated

This sort of approach results in a formula for the solution known as Cramer's Rule.

  y = (fa-cd)/(ae-bd)

The corresponding solution for x is ...

  x = (ce-bf)/(ae-bd)

__

The point of looking at the equations first is that you can often choose which variable to eliminate and what multiplier to use to minimize the amount of arithmetic involved—as we did above.

sweet-ann [11.9K]3 years ago
4 0

Answer: x = 4

y = - 3

Step-by-step explanation:

The system of simultaneous linear equations is expressed as

x - 3y = 13 - - - - - - - - - - - - - - 1

2x + 4y = - 4 - - - - - - - - - - - - - 2

We would eliminate x by multiplying equation 1 by 2 and equation 2 by 1. It becomes

2x - 6y = 26 - - - - - - - - - - - -3

2x + 4y = - 4- - - - - - - - - - - - -4

Subtracting equation 4 from equation 3, it becomes

- 6y - 4 y = 26 - - 4

- 10y = 30

Dividing the left hand side and the right hand side of the equation by - 10, it becomes

- 10y/- 10 = 30/-10

y = - 3

Substituting y = - 3 into equation 1, it becomes

x - 3 × - 3 = 13

x + 9 = 13

Subtracting 9 from the left hand side and the right hand side of the equation, it becomes

x + 9 - 9 = 13 - 9

x = 4

You might be interested in
Find cos(2theta) if cos(theta)= 3/4
yuradex [85]
Sin theta = 8/17 and theta is in the second quadrant. Find sin(2theta),cos(2theta),tan(2theta) exactly sin(2theta) cos(2theta) tan(2theta) sin(2theta) would it be 2 x (8/17) cos(2theta) would be 2 x (15/17) tan(2theta) would be 2 x (8/17 divided by 15/17) is this correct?
6 0
3 years ago
What is equivalent to 4^3*4^x
KatRina [158]
4^x+3 (the x + 3 is included in the power). That's just another way that you could write that.
8 0
3 years ago
The graph of the function B is shown below. find B(1).
Furkat [3]

Answer:

B(1) = 2

Step-by-step explanation:

Function B(x), according to the graph, which point has an x-value of 1? Point (1, 2). So the solution is 2.

4 0
3 years ago
75 points urgent.Jenny&amp;Natasha are working on a problem together: Solve 3+8=−2. Natasha thinks the first step is to multiply
Bad White [126]

Answer:

−2x3

Step-by-step explanation:

i solved the equation then multiplied by 3

5 0
3 years ago
Can the numbers 24,32,40 be the lengths of three sides of a right triangle?
Naddika [18.5K]

Answer:

Yes

Step-by-step explanation:

using pythagorus theorum:   a^{2} + b^{2} = c^{2}

24^{2} +32^{2} =  1024+576

                        =   1600

40^{2} = 1600

thus, it can be concluded that these lengths can be the sides of a right-angled triangle.

5 0
3 years ago
Other questions:
  • Need help on this ASAPPPPP
    10·2 answers
  • Can someone please tell me what the formula to find area and volume for this would be?
    7·1 answer
  • Select ALL the expressions that are equal to 3(n+4) *
    13·2 answers
  • Five years ago, an alligator was 2 1/6 feet long. Today the alligator is three times longer. How long is the alligator now
    13·1 answer
  • A jar has 2 red marbles, 3 blue marbles, and 5 green marbles. Draw two marbles at random, without replacement. What is the chanc
    5·1 answer
  • The list price of a diamond ring is $662. The jeweler is offering a chain discount of 15% less 10%. What is the final net price
    8·1 answer
  • Help finding the shaded area
    7·1 answer
  • What is the coordinate of the midpoint of WQ?
    11·1 answer
  • A baseball stadium sells a slushy cup for $5 and $1 for every time you fill it. How much would you pay in total to drink slushy
    9·1 answer
  • Look at image please
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!