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Answer:
The lines intersect at x = 1.5 and y = 1
Step-by-step explanation:
We need to find the intersection of the lines 2x+5y=8 and 6x+y=10.
We need to find the values of x and y by elimination and by substitution.
a) By Elimination:
2x+5y = 8 (1)
6x + y = 10 (2)
Multiply eq(2) with 5 and subtract eq(1) from(2)
30x + 5y = 50
2x + 5y = 8
- - -
___________
28x = 42
x = 1.5
Now putting value of x in eq(2)
6x + y = 10
6(1.5) + y = 10
9 + y = 10
=> y = 10 - 9
y = 1
so, (x,y) = (1.5,1)
The lines intersect at x = 1.5 and y = 1
b) By substitution
2x+5y = 8 (1)
6x + y = 10 (2)
Finding value of y in equation 2 and substituting in eq(1)
y = 10 -6x
2x + 5(10 - 6x) = 8
2x + 50 - 30x = 8
-28x = 8-50
-28x = -42
x = -42/-28
x = 1.5
Now finding value of y by substituting value of x
6x + y = 10
6x = 10-y
x = 10 - y /6
2x + 5y = 8
2(10-y/6) + 5y = 8
10-y/3 + 5y = 8
10 -y +15y/3 = 8
10 +14y = 8*3
+14 y = 24 -10
+14 y = 14
y = 14/14
y = 1
So, (x,y) = (1.5,1)
The lines intersect at x = 1.5 and y = 1
