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3 years ago

How to solve a system of three equations with substitution

Mathematics

1 answer:

zloy xaker [14]3 years ago

4 0

Answer:

Usually there are the variables x y z but it doesn't matter what they are.

Step-by-step explanation:

First choose your first variable to solve. Find x by putting all the numbers and variables to one side.

once you found x substitute the answer for x in all the equations. Next find y and substitute your answer in all the equations again.

Once you have solved 2 variables then you are able to solve z.

If you have questions please feel free to ask in the comments below.

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Which of the following inequalities has no solutions?

neonofarm [45]

Answer:

A) x > 3 and x < 2 has no solutions

Step-by-step explanation:

Given inequalities below and we are looking for a pair with no solution.

Let's verify:

A) x > 3 and x < 2,

It has no solutions since the two inequalities have no common interval.

B) x > - 3 and x < - 2,

Its solution is -3 < x < - 2, the interval between two given endpoints.

C) x > - 3 and x < 2,

Similar to option B, the interval is between two endpoints:

- 3 < x < 2

D) x > - 3 and x > - 2,

Its solution is x > - 2, the two inequalities cover almost same interval.

8 0

1 year ago

17+8x=3x+62 if x =16

Anton [14]

X=16 would not be true because it doesn’t work. X would equal 9.

5 0

3 years ago

Suppose that Y and Z are points on a number line if YZ=20 and Y lies at 3 where could Z be located

creativ13 [48]

17? probably I think

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3 years ago

a store clerk has 45 shirts to pack in boxes each boxes hold 6 shirts what is the fewest boxes of clerk will need to pack all th

natali 33 [55]

The store clerk needs 8 boxes

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3 years ago

Dana has 800 yards of fencing to enclose a rectangular area. Find the dimensions of the rectangle that maximize the enclosed are

grin007 [14]

Answer:

Perimeter of rectangle states that total distance around the outside, which can be found by adding together the length of each side.

As per the given statement, Dana has 800 yards of fencing to enclose a rectangular area.

Therefore, perimeter of rectangle = 800 yards.

Perimeter(P) of rectangle is given by :

P = 2(x+y) where x is the length and y is the width of the rectangles respectively.

Then,

2(x+y) = 800

Divide both sides by 2 we get;

x+y =400

y = 400 -x .....[1]

We know, the area(A) of rectangle is given by

A = xy .....[2]

Substitute equation [1] into [2] we get;l

A = x(400-x)

using distributive property $a\cdot (b+c) = a\cdot b+ a\cdot c$

$A = 400x -x^2$

$A =-x^2+400x$ ......[3]

To maximize the enclosed area.

For a quadratic function in standard form $y =ax^2+bx+c$ , the axis of symmetry is a vertical line given by;

$x = -\frac{b}{2a}$

Then; we have from equation [3]

a = -1 and b = 400

By axis of symmetry;

$x = -\frac{b}{2a}$ = $-\frac{400}{2 \cdot -1} =\frac{400}{2} = 200$

Substitute in equation [1] to solve for y:

y = 400 - 200 = 200

The dimensions of the rectangle that maximize enclosed area are:

x = 200 units and y = 200 units.

Maximum area = $200 \times 200 = 40,000$ square units.

We can say that maximum area of rectangle will always be a square

4 0

2 years ago