Solve and Check using the removal method:

Mathematics

1 answer:

Luba_88 [7]3 years ago

8 0

9514 1404 393

Answer:

(x, y) = (2, 3)

Step-by-step explanation:

"Removal method" is a new one for me. We presume it is another name for the "elimination" or "addition" method.

Multiply the second equation by 5 and add the first.

(6x -5y) +5(-4x +y) = (-3) +5(-5)

-14x = -28 . . . . . simplify

x = 2 . . . . . . . . . divide by -14

-4(2) +y = -5 . . . substitute for x in the second equation

y = 3 . . . . . . . . . add 8

The solution is (x, y) = (2, 3).

<em>Check</em>

We found y using the second equation, so we know the values of x and y work in that one. We only need to check the values in the first equation.

6(2) -5(3) = -3

12 -15 = -3 . . . . . true; answer checks OK

You might be interested in

which of the following is an equation of a line parallel to the equation <img src="https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B

kotykmax [81]

Answer:

Any equation of a line having a slope of 1/2.

Step-by-step explanation:

It appears that the question gives answer choices and this problem could have many solutions, but parallel lines have equal slopes. The slope of this line is 1/2 since it is in y=mx+b form where m is the slope. So a few examples of equations of lines parallel to the given equation would be y = 1/2x - 5 or y = 1/2x + 10 etc.

7 0

3 years ago

Given the graph of a function f. Identify the function by name. Then Graph, state domain & range in set notation:A) f(x) +2B

WARRIOR [948]

The function in the graph has the name of square function.

The domain of a function is all values of x the function can have. The domain of this function is all real numbers:

$\mleft\lbrace x\in\R\mright\rbrace$

The range of a function is all values of y the function can have. The range of this function is all positive numbers, including zero:

$\mleft\lbrace y\in\R\mright|y\ge0\}$

In order to graph f(x) + 2, we just need to translate the graph 2 units up. To find the new points, we need to increase all y-coordinates by 2:

(-2, 6), (-1, 3), (0, 2), (1, 3), (2, 6)

Domain: {x ∈ ℝ}

Range: {y ∈ ℝ | y ≥ 2}

Then, in order to graph f(x) - 2, we just need to translate the graph 2 units down. To find the new points, we need to decrease all y-coordinates by 2:

(-2, 2), (-1, -1), (0, -2), (1, -1), (2, 2)

Domain: {x ∈ ℝ}

Range: {y ∈ ℝ | y ≥ -2}