Consider the system of equations 2x + 3y = 8 and 4x – 2y = 4. Find the point of intersection for this system of equations and explain what the coordinates of that point represent.

Answer 1

To find the point of intersection for the system of equations, we can solve the system using the method of substitution or elimination.

Using the method of elimination:

Multiply the first equation by 2 and the second equation by 1 to make the coefficients of x in both equations the same:

2(2x + 3y) = 2(8) -> 4x + 6y = 16
1(4x – 2y) = 1(4) -> 4x – 2y = 4

Subtracting the second equation from the first equation eliminates x:

(4x + 6y) - (4x – 2y) = 16 - 4
4x + 6y - 4x + 2y = 12
8y = 12
y = 12/8
y = 3/2

Substituting this value of y back into one of the original equations, we can solve for x:

2x + 3(3/2) = 8
2x + 9/2 = 8
2x = 8 - 9/2
2x = 16/2 - 9/2
2x = 7/2
x = 7/2 * 1/2
x = 7/4

Therefore, the point of intersection for this system of equations is (x, y) = (7/4, 3/2).

The coordinates of this point represent the values of x and y that satisfy both equations simultaneously. In other words, substituting these values for x and y into either of the original equations will make each equation true.