If fx 2x 5 and gx 3x 2 what are the coordinates of the p

If f(x) = 2x - 5, and g(x) = 3x + 2, what are the coordinates of the point at which f(x) intersects g(x)?

Solution

f(x) = 2x - 5

g(x) = 3x + 2

for finding the intersection point of these lines, we can equate these f(x) and g(x) to find x-cordinate // at intersection point the x and y coordinates will be equal

f(x) = g(x)

2x-5 = 3x+2

suntracting 3x on both sides

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

-x -5 = 2

now we add +5 on both sides

-x -5 +5 = 2+5

-x = 7

we can multiply both sides by \"-1\"

x = -7

now we can caluclate the y cordinate of this intersection point

put x = -7 in f(x) or g(x)

f(x) = 2*(-7) -5

f(-7) = -14 -5

f(-7) =-19            // y-cordinate