MATH SOLVE

2 months ago

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

Accepted Solution

A:

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 = 100Β

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 :)

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 = 100Β

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 :)