Answer for Question (1):
The system of equations: x+3y=6
2x-y=10
Solve the first equation x+3y=6 for y:
Subtracting x on both sides,
x+3y-x=6-x
3y=6-x
Now dividing 3 on both sides, we get
y=2-x/3 = negative one third x + 2
Thus y= negative one third of x +2
Answer for question (2):
The system of equation :
5x-3y=-3 --> (1)
2x-6y=-6 -->(2)
Multiply equation (1) by 2, we get 10x-6y=6.
Subtracting (1) by (2), we get 8x=0 implies x=0.
Plug in x=0 in equation (1), 0-3y=-3
Dividing -3 on both sides,
y=-3/-3=1
So the solution of y is 1.
Answer for Question (3):
System of equation:
7x-2y=-3 (1)
14x+y=14 (2)
Multiply (2) by 2,
28x+2y=28 (3)
Adding (1) and (3), we get 35x=25
Now dividing 35 on both sides, x=25/35=5/7.
Plug in x=5/7 in equation (1), we get 5-2y=-3
-2y=-3-5
-2y=-8
Dividing -2 on both sides,
y=4
Thus the solution of this system of equation as (5/7,4).
Answer for question (4):
x + 3y = 9 ---> (1)
3x − 3y = −13 ---> (2)
Adding equation (1) and (2), we get
4x=-4
Dividing 4 on both sides,
x=-1
Plug in x=-1 in equation (1), we get
-1+3y=9
Adding 1 on both sides,
3y=9+1=10
Now dividing 3 on both sides,
y=10/3.
so the solution is (-1,10/3).
Answer for question (5):
System of equation is 4x − y = 3 (1)
7x − 9y = −2 (2)
consider the first equation 4x-y=3
Adding y on both sides, 4x=3+y
subtracting 3 on both sides, we get y=4x-3
Substitute y=4x-3 in equation (2),
7x-9(4x-3)=-2
7x-36x+27=-2
Combine the like terms,
-29x+27=2
Adding 27 on both sides,
-29x=-29
dividing -29 on both sides,
x=1
Plug in x=1 in y=4x-3,
y=4(1)-3=1
Then the solution is (1,1).
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