Question

24.7. 1) { х+20у=37, 5у+х=7 2) {у-8х=-33, 7х-у=29 3) { 17 х +у =90 у - 23 х =-110​

Answer 1

Ответ:

1) (-3;2)

2)(4;-1)

3)(5;5)

Объяснение:

Answer 2

To solve these systems of equations, you can use either the substitution method or the elimination method. I'll show you how to solve each of them using the elimination method:

1. { x + 20y = 37 5y + x = 7

First, you can subtract the second equation from the first equation to eliminate x:

(x + 20y) - (5y + x) = 37 - 7

This simplifies to:

15y = 30

Now, divide both sides by 15 to solve for y:

y = 30 / 15 y = 2

Now that you have the value of y, you can substitute it into one of the original equations to solve for x. Let's use the second equation:

5y + x = 7 5(2) + x = 7

Now, solve for x:

10 + x = 7

Subtract 10 from both sides:

x = 7 - 10 x = -3

So, the solution to the first system of equations is x = -3 and y = 2.

2. { y - 8x = -33 7x - y = 29

To eliminate y, add the two equations together:

(y - 8x) + (7x - y) = -33 + 29

This simplifies to:

-8x + 7x = -4

Combine like terms:

-x = -4

Now, divide both sides by -1 to solve for x:

x = 4

Now that you have the value of x, you can substitute it into one of the original equations to solve for y. Let's use the first equation:

y - 8x = -33 y - 8(4) = -33

Now, solve for y:

y - 32 = -33

Add 32 to both sides:

y = -33 + 32 y = -1

So, the solution to the second system of equations is x = 4 and y = -1.

3. { 17x + y = 90 y - 23x = -110

To eliminate y, add the two equations together:

(17x + y) + (y - 23x) = 90 - 110

This simplifies to:

-6x = -20

Now, divide both sides by -6 to solve for x:

x = -20 / -6 x = 10/3

Now that you have the value of x, you can substitute it into one of the original equations to solve for y. Let's use the first equation:

17x + y = 90 17(10/3) + y = 90

Now, solve for y:

(170/3) + y = 90

Subtract (170/3) from both sides:

y = 90 - (170/3)

To subtract fractions, find a common denominator:

y = (270/3) - (170/3)

Now, subtract the numerators:

y = (270 - 170) / 3 y = 100 / 3

So, the solution to the third system of equations is x = 10/3 and y = 100/3.