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jekas [21]
3 years ago
9

How many solutions does the system have?

Mathematics
1 answer:
umka21 [38]3 years ago
3 0

One solution

<h2>Explanation:</h2>

For a system of linear equations in two variables, we could have three possible cases:

<h3>Case 1. No solution.</h3>

This happens when the lines are parallel and have different y-intercepts.

<h3>Case 2. One solution.</h3>

This happens when the lines intersect at a single point.

<h3>Case 1. Infinitely many solutions</h3>

This happens when the lines are basically the same having the same slope and y-intercept.

So, let's rewrite our lines in Slope-intercept form y=mx+b:

Line \ 1: \\ \\  4x-2y = 8 \\ \\ 2y=4x-8 \\ \\ y=\frac{4}{2}x-\frac{8}{2} \\ \\ y=2x-4 \\ \\ \\ Line \ 2: \\ \\ 2x + y = 2 \\ \\ y=-2x+2

As you can see, they have different slopes and y-intercepts. So they will intersect at a single point which is the solution of the system. By using graphing tool we get that this point is (1.5, -1) as indicated in the figure below.

<h2>Learn more:</h2>

Parametric equations: brainly.com/question/10022596

#LearnWithBrainly

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Confidence interval standard deviation;

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Step-by-step explanation:

Given :

Variance, s² = 34.34

Standard deviation, s = 5.86

Sample size, n = 27

Degree of freedom, df = 27 - 1 = 26

Using the relation for the confidence interval :

[s²(n - 1) / X²α/2, n-1] ; [s²(n - 1) / X²1-α/2, n-1]

From the chi distribition table :

X²α/2, n-1 = 41.923 ; X²1-α/2, n-1 = 13.844

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[21.297 ; 64.493]

The 95% confidence interval for the population variance is :

21.297 < σ² < 64.493

Standard deviation is the square root of variance, hence,

The 95% confidence interval for the population standard deviation is :

4.615 < σ < 8.031

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