Question

Question 3 (10 %) Find out the solution to x and y for the system of equations: 1. 2x-8y=11 and 9x+3y=5​

Answer 1

x = 73/78

y = -89/78

Explanation:

system of equations

2x - 8y = 11

9x + 3y = 5

3y = 5 - 9x

y = 5/3 - 3x

substitute new value

2x - 8(5/3 - 3x) = 11

2x - 40/3 + 24x = 11

26x - 40/3 = 11

26x = 11 + 40/3

26x = 73/3

x = (73/3)/26

x = 73/78

plug in value for x

9(73/78) + 3y = 5

219/26 + 3y = 5

5 - 219/26 = 3y

3y = -89/26

y = -89/78

Answer 2

To find the solution for x and y, we can use the method of substitution or elimination. Let's use the method of elimination:

1. Multiply the first equation by 9 and the second equation by 2 to make the coefficients of x in both equations the same:
18x - 72y = 99
18x + 6y = 10

2. Subtract the second equation from the first equation to eliminate x:
(18x - 72y) - (18x + 6y) = 99 - 10
18x - 72y - 18x - 6y = 89
-78y = 89

3. Solve for y:
-78y = 89
y = 89 / (-78)
y = -1.141

4. Substitute the value of y back into one of the original equations to solve for x. Let's use the first equation:
2x - 8(-1.141) = 11
2x + 9.128 = 11
2x = 11 - 9.128
2x = 1.872
x = 1.872 / 2
x = 0.936

Therefore, the solution to the system of equations is x = 0.936 and y = -1.141.