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

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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