Mathematics, 02.07.2019 13:00, ashcookie27

What is the solution to the system of equations using the linear combination method? {3x+y=42x+y=7 (−1, 7) (−3, 12) (−3, 13) (0, 4)

Answers: 1

Show answers

Answers

answered: lashayl27

(-3, 13)

Explanation:

We can subtract the second equation from the first to eliminate the y-variable.

... (3x +y) -(2x +y) = (4) -(7)

... x = -3 . . . . . simplify

Using either equation, we can find y.

... 3x +y = 4 . . . . the first equation

... y = 4 -3x = 4 -3(-3) = 13 . . . . . the first equation rearranged by subtracting 3x

The solution is (x, y) = (-3, 13).

Comment on the solution

The coefficient of y is 1 in both equations. This means that multiplying one of the equations by -1 and adding that result to the other will make the y-terms add to zero (cancel). This is the goal of "linear combination": cancel one of the variables.

Another combination we could have used is multiplying the first equation by -2/3 and adding to the second. This would cancel the x-terms.

Generally, we prefer to work with integers, so if we actually wanted to cancel x-terms, we would likely multiply the second equation by 3 and the first equation by -2, then add the results of those operations. This would give

... 3(2x +y) -2(3x +y) = 3(7) -2(4)

... y = 13 . . . . . simplify

You will note that the choice of multipliers made 3(2x) the opposite of -2(3x), so when these products are added, the result is zero. That is the reason behind the choice of multipliers. As a starting point, you can choose the multipliers to be the cofficient of the variable in one equation, and the opposite of the coefficient of the variable in the other equation.

Here, x-coefficients are 3 and 2; the multipliers we chose were -2 and 3. (The reason for not using 2 and -3 is that we want a positive coefficient for y when we're done simplifying.)

answered: Guest

hi,

i'm 75% sure the answer is 1,1 to both lines.

have a great day

answered: Guest

the formula of a slope:

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

from a table we have

$x_1=-4,\ y_1=7\\\\x_2=-2,\ y_2=5$

substitute:

$m=\dfrac{5-7}{-)}=\dfrac{-2}{2}=-1$

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0

answer: the function g(x) has the greatest slope.
The functions, f(x) and g(x) , are shown below. x f(x) -4 7 -2 5 0 3 2 1 4 -1 which function has the

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 20:00, yokis2710

If the sales price of a dvd is $20 and the markup is 34%, what is the cost of the dvd?

Answers: 1

continue

Mathematics, 21.06.2019 20:30, afitzgerald

Sketch the region enclosed by the given curves. decide whether to integrate with respect to x or y. draw a typical approximating rectangle and label its height and width. y= 5x, y=7x^2then find the area s of the region.

Answers: 3

continue

Mathematics, 21.06.2019 20:30, nsbegay2007

Tom is the deli manager at a grocery store. he needs to schedule employee to staff the deli department for no more that 260 person-hours per week. tom has one part-time employee who works 20 person-hours per week. each full-time employee works 40 person-hours per week. write and inequality to determine n, the number of full-time employees tom may schedule, so that his employees work on more than 260 person-hours per week. graph the solution set to this inequality.

Answers: 2

continue

Mathematics, 22.06.2019 00:00, mwest200316

Ineed with the quizzes in apex mathematics ii

Answers: 1

continue

Do you know the correct answer?

What is the solution to the system of equations using the linear combination method? {3x+y=42x+y=7...