Giải hệ phương trình

To solve the system of equations, we can use the method of substitution or elimination. Let's solve the system of equations step by step:

a) x - y = 3
b) x + 3y = 5

From equation a), we can rewrite it as x = y + 3 and substitute it into equation b):
(y + 3) + 3y = 5
4y + 3 = 5
4y = 2
y = 0.5

Now, substitute y = 0.5 back into x = y + 3:
x = 0.5 + 3
x = 3.5

Therefore, the solution to equations a) and b) is x = 3.5, y = 0.5.

c) 2x + y = 3
d) 2x + y = 5

These two equations are inconsistent because they represent parallel lines that will never intersect. Therefore, there is no solution to this system of equations.

e) x + y = 9
f) x - 2y = 7

From equation e), we can rewrite it as x = 9 - y and substitute it into equation f):
9 - y - 2y = 7
9 - 3y = 7
-3y = -2
y = 2/3

Now, substitute y = 2/3 back into x = 9 - y:
x = 9 - 2/3
x = 25/3

Therefore, the solution to equations e) and f) is x = 25/3, y = 2/3.

h) 5(x + 2y) - 3(x - y) = 99
3x + 2y = 5
2x + 5y = 9
x - 3y = -2
x + y = 3
x - 3y = 7x - 4y - 17

These equations form a system that can be solved using the method of substitution or elimination. Let's solve them step by step.