Question

What is the point of intersection of these two lines:25x+10y=10010x+20y=120

Answer 1

Answer:
The point of intersection is (2,5)

Explanation:
To get the point of intersection, we would need to solve the two equations simultaneously. This is because, the point of intersection satisfies both equations.
The first given equation is:
25x + 10y = 100 ..........> equation I
The second given equation is:
10x + 20y = 120
Divide all terms by 10 to simplify, this would given us:
x + 2y = 12
This equation can be rewritten as:
x = 12 - 2y ...........> equation II

Substitute with equation I in equation II and solve for y as follows:
25x + 10y = 100 
25(12-2y) + 10y = 100
300 - 50y + 10y = 100
300 - 40y = 100
300 - 100 = 40y
40y = 200
y = 200 / 40
y = 5
Substitute with y in equation II to get x as follows:
x = 12 - 2y
x = 12 - 2(5)
x = 12 - 10
x = 2

Based on the above, the solution to the system of equations which also represents the point of intersection between the two lines would be (2,5)

Hope this helps :)