y=2
x=3
Step-by-step explanation:
make x - y = 1 into x= y + 1
put that wherever x is in the other equation
so y + 1 + 2y =7. then combine like terms into 3y =6. then divide 6 by 3 so you get y = 2
then substitute 2 into the y in the equation x - y = 1 and you get x = 3
METHOD OF ELIMINATION:
Given pair of linear equations are:
x+2y= 7 β β β Eqn(i)
On comparing with a1x+b1y+c1 = 0
a1 = 1, b1 = 2, c1 = -7x-y = 1 β β β Eqn(ii)
On comparing with a2x+b2y+c2 = 0
a2 = 1, b2 = -1 , c2 = -1a1/a2 = 1/1 = 1
b1/b2 = 2/-1 = -2
c1/c2 = -7/-1 = 7
We have,
a1/a2 β b1/b2 β c1/c2
So, Given pair of linear equations in two variables have a unique solution.
Now,
On Subtracting eqn(ii) from eqn(i) then
x+2y = 7
x-y = 1
(-)
0 +3y = 6
β 3y = 6
β y = 6/3
β y = 2
On Substituting the value of y in (1) then
β x-2 = 1
β x = 1+2
βx = 3
Answer: Therefore , the value of x and y with be (3,2) respectively.
Additional comment:
If aβx+bβy+cβ = 0 and aβx+bβy+cβ = 0 are pair of linear equations in two variables thenIf aβ/aβ β bβ/bβ β cβ/cβ then they are Consistent and independent lines or Intersecting lines and they have a unique solution.If aβ/aβ = bβ/bβ = cβ/cβ then they are Consistent and dependent lines or Coincident lines and they have infinitely number of many solutions.If aβ/aβ =bβ/bβ β cβ/cβ then they are Inconsistent lines or Parallel lines lines and they have no solution.c square
Step-by-step explanation: