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2 years ago

Does the ordered pair (2,1) satisfy the following system of equations?

Mathematics

1 answer:

love history [14]2 years ago

6 0

To determine the whether the ordered pair satisfies the equation:

⇒ we must plug in the values

⇒ since coordinates are (x,y) ⇒ (2,1)

⇒ there we must plug 2 into the 'x' position in the equation

⇒ and 1 into the 'y' position in the equation

Let's try the first equation:

$3x-y=5\\3(2)-1=5\\6-1=5\\5=5$

Ordered pair satisfies first equation

Let's try the second equation

$5x-2y=8\\5(2)-2(1)=8\\10-2=8\\8=8$

Ordered pair satisfies second equation

Thus ordered pair satisfies the following system of equations

Answer: Yes

Hope that helps!

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3 years ago

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3 years ago

Solve for the unknown length.

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<h2>Similar Triangles</h2>

Similar triangles have the same proportions of sides, but they have different side lengths.

To solve for missing sides in similar triangles, we can set up a proportion.

For instance, let's say that side a in Triangle A corresponds with side b in Triangle B. Let's say that side h in Triangle A also corresponds with side k in Triangle B. Then, it would be true that:

$\dfrac{a}{b}=\dfrac{h}{k}$

We need to make sure of a couple things:

The numerators and denominators of fractions are corresponding
The numerators describe one triangle, and the denominators describe another (can't switch, otherwise the calculations will get messed up)

<h2>Solving the Question</h2>

We're given two triangles (do you see it?).

Triangle ABC
Triangle ADE

These two triangles are similar.

We must solve for the length of side BC in Triangle ABC.

We're given the length of DE, the corresponding side in Triangle ADE.
We're also given the lengths of bottom sides, 20 units and 30 + 20 = 50 units.

Set up a proportion:

$\dfrac{x}{15}=\dfrac{50}{20}\\\\\dfrac{x}{15}=\dfrac{5}{2}\\\\x=\dfrac{5}{2}*15\\\\x=\dfrac{75}{2}\\\\x=37.5$

Therefore, the unknown length is 37.5 units.

<h2>Answer</h2>

37.5 units

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1 year ago