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3 years ago

Solve the system by using the technique of ‘elimination’: -2x+5y=-42,7x+2y=30

Mathematics

1 answer:

Gekata [30.6K]3 years ago

3 0

Solve the following system using elimination:

{5 y - 2 x = -42 | (equation 1)

7 x + 2 y = 30 | (equation 2)

Swap equation 1 with equation 2:

{7 x + 2 y = 30 | (equation 1)

-(2 x) + 5 y = -42 | (equation 2)

Add 2/7 × (equation 1) to equation 2:

{7 x + 2 y = 30 | (equation 1)

0 x+(39 y)/7 = (-234)/7 | (equation 2)

Multiply equation 2 by 7/39:

{7 x + 2 y = 30 | (equation 1)

0 x+y = -6 | (equation 2)

Subtract 2 × (equation 2) from equation 1:

{7 x+0 y = 42 | (equation 1)

0 x+y = -6 | (equation 2)

Divide equation 1 by 7:

{x+0 y = 6 | (equation 1)

0 x+y = -6 | (equation 2)

Collect results:

Answer: {x = 6, y = -6

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vampirchik [111]

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Step-by-step explanation:

The distance formula states that the distance between two points $(a,b)$ and $(c,d)$ is $\sqrt{(a-c)^2+(b-d)^2}$ .

The two points we have are $(4,6)$ and $(-4,-3)$ . Plugging these numbers into the distance formula, we have

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Squaring and adding gives

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which is the answer in simplest form. This also rounds to about 12.04.

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