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mash [69]
3 years ago
14

Tell whether the ordered pair is a solution of the system of linear equations.

Mathematics
1 answer:
Lana71 [14]3 years ago
4 0

To figure out if the ordered pairs are a solution to the equations, you would need to plug in the points. Your points are ordered as (x,y)

You would plug in the number that's in the x spot in x, and the number in the y spot in y.

Let's start of with the first problem:

First thing you would do is plug in (-1) to x, and 6 to y.

Your equations would look like this:

6(-1) + 3(6) = 18

2(-1) + 6 = 7

What you would now do is solve the equations. When you solve them, you would get these answers

12 = 18

4 = 7

For #1, it would be no solution because the numbers do not equal each other. (Fun fact) If one of them ends up as a solution, but the other is no solution, the answer would be no solutions because BOTH of them have to be a solution to the equations given in order to be a solution.

If you do the same strategy, (plugging in the numbers to x and y), you would get the rest of the answers for the problems.

I hope this helps, if you need any more assistance, I would be glad to help!




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Step-by-step explanation:

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Which equation is a point slope form equation for line AB ?
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Answer:

Answer choice D:

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Step-by-step explanation:

This question is basically asking you to find the point-slope form equation for a line going through the points (3, 2) and (5, 6).

As you can tell by the name, point-slope form needs both a point that the line goes through and the slope of the line.

You can find the slope of the line by using the slope formula since you have two points that the line goes through.

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Substitute in the points A and B into the formula.

m=\frac{6-2}{5-3} \rightarrow\frac{4}{2} \rightarrow 2

The slope of this line is 2.

Now since we have the slope and a point of the line, we can plug this into the point-slope form equation, which is y - y1 = m(x - x1).

We will be using one of the points (I will be using point A) to substitute the coordinates into y1 and x1, and using the slope to substitute into m.

Substitute point A's coordinates and the slope of the line into the point-slope form equation.

y - (2) = 2(x - (3))

I always put parentheses around the numbers I substitute into an equation to see exactly what is being plugged in, but now you can remove them to find your answer.

y - 2 = 2(x - 3)

Now, since none of the answer choices do not fit with the answer we have found, we can use the other point coordinate-- point B.

Substitute point B and the slope 2 into the equation.

y - (6) = 2(x - (5))

Remove the parentheses.

y - 6 = 2(x - 5)

There is an answer choice for this answer we have found, answer choice D.

By the way, both of the equations we found: y - 2 = 2(x - 3) and y - 6 = 2(x - 5) will yield the same answer in the end so don't worry if one of the points don't work if you have a multiple choice like this question.

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