Question

point of intersection for y=-2/3x+2 and y=-3x+5

Answer 1

To find the point of intersection for the two equations y= -2/3x + 2 and y= -3x + 5, we can set the two equations equal to each other:

-2/3x + 2 = -3x + 5

Now, we can simplify and solve for x:

-2/3x + 2 = -3x + 5
Multiply both sides by 3 to get rid of the fraction:
-2x + 6 = -9x + 15
Add 9x to both sides:
7x + 6 = 15
Subtract 6 from both sides:
7x = 9
Divide by 7:
x = 9/7

Now that we have found the x-coordinate, we can plug this value back into one of the original equations to find the y-coordinate. Let's use the first equation y = -2/3x + 2:

y = -2/3(9/7) + 2
y = -6/7 + 14/7
y = 8/7

Therefore, the point of intersection for the two equations y= -2/3x + 2 and y= -3x + 5 is (9/7, 8/7).