Question

1280. 1) 10(x + y) = 30 + 8x, [21(x 2) 9(x - y) = -49 - 8y; - y) = 48 + 20 x, 19(y + x) = 100 + 12y.
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Answer 1

Ответ:

There are three equations given:

1. 10(x+y)=30+8x

2. 21(x^2)9(x - y) =-49-8y

3. 19(y + x)=100+12y

To solve for x and y, we can use substitution and elimination methods.

Substitution Method:

1. From equation 1, we can simplify it to get x in terms of y:

10x + 10y = 30 + 8x

2x = 30 - 10y

x = 15 - 5y

2. Substitute this value of x into equation 2:

21[(15 - 5y)^2] - 9(15 - 5y)y = -49 - 8y

3. Simplify and solve for y:

441 - 210y + 25y^2 - 135y + 45y^2 = -49 - 8y

70y^2 - 67y - 490 = 0

Using the quadratic formula, we get:

y = (-(-67) ± sqrt((-67)^2 - 4(70)(-490))) / (2*70)

y = (-(-67) ± sqrt(59289)) / 140

y ≈ -2.43 or y ≈ 3.50

4. Substitute the values of y into equation 1 to solve for x:

If y ≈ -2.43, then x ≈ 27.15

If y ≈ 3.50, then x ≈ -13.50

Elimination Method:

1. Multiply equation 1 by 9 and equation 3 by -8 to eliminate y:

90x + 90y = 270 + 72x

-152y - 152x = -800 - 96y

2. Add the two equations together to eliminate x:

-62y = -530

y = 8.55

3. Substitute this value of y into equation 1 or 3 to solve for x:

Using equation 1: x ≈ -0.35

Using equation 3: x ≈ -4.86

Therefore, there are multiple solutions for the given system of equations.

Using substitution method, we get two solutions:

(x ≈ 27.15, y ≈ -2.43) and (x ≈ -13.50, y ≈ 3.50)

Using elimination method, we get two solutions:

(x ≈ -0.35, y ≈ 8.55) and (x ≈ -4.86, y ≈ 8.55)

Пошаговое объяснение:

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