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3 years ago

What does it mean for an ordered pair (x,y) to be a solution to a system of equations?

Mathematics

1 answer:

Andrew [12]3 years ago

7 0

Answer:

For an ordered pair to be a solution to a system of equations, the values for x and y must agree with every equation in the system. For example, if you have two linear equations so that their lines intersect, then there is exactly one solution (x, y) such that both equations are true statements when both x and y are entered into both equations. Therefore, those two coordinates (x, y) are the only solution to that system.

In other systems, such as quadratic systems containing two equations with two second-degree variables, x^2 and y^2, you can have up to four solutions (x, y) since the graphs of these equations may intersect in up to four points. Again, it means that the coordinates to each of these points agree with all equations in the system.

Step-by-step explanation:

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ozzi

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3 years ago

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Logarithmic form x^19 = y

arlik [135]

Log properties or log transformation is;

b ^ x = a , then to solve for the exponent x, log b a = x or read as log a base b = x.

 x^19 = y

x = b
a = y
x = 19

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4 0

3 years ago

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Please help me out with this equation! i will mark as brainliest

Natali [406]

Answer: Choice D

y = -(x - 2)^2 + 7

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Explanation:

The highest point is (2, 7) so this is the vertex.

In general, the vertex is (h, k). We can say that h = 2 and k = 7.

The vertex form

y = a(x-h)^2 + k

updates to

y = a(x-2)^2 + 7

----------------

Note that the graph goes through (0,3) which is the y intercept. Plug those x,y coordinates into the equation above to solve for 'a'

y = a(x-2)^2 + 7

3 = a(0-2)^2 + 7

3 = a(-2)^2 + 7

3 = a(4) + 7

3 = 4a + 7

4a+7 = 3

4a = 3-7

4a = -4

a = -4/4

a = -1

----------------

Therefore, we have

y = a(x-2)^2 + 7

update to

y = -1(x-2)^2 + 7

which is the same as

y = -(x - 2)^2 + 7

and that's why the answer is choice D

4 0

3 years ago

Read 2 more answers

PLEASE HELP!! solve |2x-2| ≥6.

Anastaziya [24]

<h3>Answer:</h3>

x ≤ -2 OR x ≥ 4

__________________________________________________________

<h3>Step-by-step explanation:</h3>

We are given the inequality:

|2x - 2| ≥ 6

Getting rid of the Modulus:

Since 2x-2 is in modulus:

|2x-2| = -(2x-2) OR 2x-2

(since the modulus of both these values is 2x-2)

Hence, our inequality can be written in 2 different ways:

2x-2 ≥ 6 (if 2x-2 ≥ 1)
-(2x - 2) ≥ 6 (if 2x-2 < 0)

__________________________________________________________

Solving these 2 inequalities:

Solving inequality 1:

2x - 2 ≥ 6

2x ≥ 8 [adding 2 on both sides]

x ≥ 4 [dividing both the sides by 2]

This is the solution of the inequality if: 2x-2 ≥ 0

Solving Inequality 2:

-(2x-2) ≥ 6

It can be rewritten as:

2 - 2x ≥ 6

2 ≥ 6 + 2x [adding 2x on both the sides]

-4 ≥ 2x [Subtracting 6 from both sides]

x ≤ -2 [Dividing both sides by 2]

This is the solution of the given inequality if: 2x-2 < 0

__________________________________________________________

Solution of the given Inequality:

Therefore, the solution of the given inequality |2x-2| ≥ 6 are:

x ≥ 4 (if 2x-2 ≥ 0)

x ≤ -2 (if 2x-2 < 0)

Hence, option C is correct!

6 0

3 years ago

$1, 000 after 2 years at an interest rate of 3.0% is $ round up to the nearest cent

BaLLatris [955]

This may be a simple interest computation.

Simple Interest = Principal * interest rate * term

Principal = 1,000
interest rate = 3%
term = 2 years

Simple Interest = 1,000 * 0.03 * 2
Simple Interest = 60

Total Amount after 2 years: 1,000 + 60 = 1,060

5 0

3 years ago