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)
