Answer:
The given system of equations has solutions below:
1) The solution is (2,3)
2) The solution is ()
3) The solution is infinitely many solutions
4) No solution
Step-by-step explanation:
Given system of equation are
To solve equation by using elimination method
Multiply eqn (2) into 2
Now subtracting (1) and (3)
_________________
7x=14
x=
Substitute x=2 in equation (1)
-2+2y=4
2y=4+2
y=3
Therefore the solution is (2,3)
2) Given equation is
4y-4=x
Rewritting as below
To solve equation by using elimination method
multiply (2) into 2
Adding (1) and (3)
-2x+y=3
2x-8y=-8
________
-7y=-5
substitute in (1)
Therefore the solution is ()
3) Given equation is
equation (1) can be written as
2(3x+y)=10
3x+y=5
Therefore equations (1) and (2) are same therefore it has infinitely many solutions
4) Given equation is
multiply equation (1) into 2
To solve equation by using elimination method
subtracting (2) and (3)
-2x-4y=28
-2x-4y=12
_______
therefore it has no solution