Question

1)3х+8у=13 5х-16у=7 2)10х+15у=-45 2х-3у=33

Answer 1

1.[3x+8y=13     2    [6x+16y=26
   [5x-16=7           ⇒[5x-16y=7  ⇒ 11x=33  x=3

Answer 2

To solve the system of equations:

1. 3x + 8y = 13 5x - 16y = 7

2. 10x + 15y = -45 2x - 3y = 33

Let's solve each system one by one.

1. 3x + 8y = 13 5x - 16y = 7

We can use the method of substitution to solve this system. Solve the first equation for x:

3x = 13 - 8y x = (13 - 8y) / 3

Substitute this value of x into the second equation:

5((13 - 8y) / 3) - 16y = 7

Multiply through by 3 to eliminate the fraction:

5(13 - 8y) - 48y = 21 65 - 40y - 48y = 21 -88y = 21 - 65 -88y = -44 y = (-44) / (-88) y = 0.5

Substitute this value of y back into the first equation to find x:

3x + 8(0.5) = 13 3x + 4 = 13 3x = 13 - 4 3x = 9 x = 3

Therefore, the solution to the first system of equations is x = 3 and y = 0.5.

2. 10x + 15y = -45 2x - 3y = 33

Let's use the method of substitution again. Solve the second equation for x:

2x = 33 + 3y x = (33 + 3y) / 2

Substitute this value of x into the first equation:

10((33 + 3y) / 2) + 15y = -45

Multiply through by 2 to eliminate the fraction:

10(33 + 3y) + 30y = -90 330 + 30y + 30y = -90 60y = -90 - 330 60y = -420 y = (-420) / 60 y = -7

Substitute this value of y back into the second equation to find x:

2x - 3(-7) = 33 2x + 21 = 33 2x = 33 - 21 2x = 12 x = 6

Therefore, the solution to the second system of equations is x = 6 and y = -7.

To summarize:

1. The solution to the first system of equations is x = 3 and y = 0.5.
2. The solution to the second system of equations is x = 6 and y = -7.