what points do these intersect

5x-2y=18
3x-3y=15

To find the points of intersection between the two lines represented by the equations 5x-2y=18 and 3x-3y=15, we can solve the system of equations. We can do this by either substitution or elimination method.

Elimination method:

Multiply the second equation by 2 to make the coefficient of y the same as the first equation:
2*(3x-3y)=2*15
6x-6y=30

Now, we have two equations with the same coefficient of y, so we can subtract them to eliminate y:
(5x-2y)-(6x-6y)=18-30
5x-2y-6x+6y= -12
-x + 4y = -12

Now, we have a new equation: -x + 4y = -12

To solve for x, isolate it by multiplying the equation by -1:
-(-x + 4y) = -12
x - 4y = 12

Now we have:
x - 4y = 12
5x - 2y = 18

Using the elimination method again, multiply the first equation by 5 and the second equation by 1:
5(x - 4y) = 5(12)
1(5x - 2y) = 1(18)
5x - 20y = 60
5x - 2y = 18

Subtract the second equation from the first equation to eliminate x:
(5x - 20y) - (5x - 2y) = 60 - 18
5x - 20y - 5x + 2y = 42
-18y = 42
y = -42/(-18)
y = 2.3333 (rounded to 4 decimal places)

Substitute y=2.3333 into one of the equations, let's use the first equation:
5x - 2(2.3333) = 18
5x - 4.6666 = 18
5x = 18 + 4.6666
5x = 22.6666
x = 22.6666/5
x = 4.5333 (rounded to 4 decimal places)

Therefore, the points of intersection are approximately (4.5333, 2.3333).