Dr. Graciela Brakus I
Nov 05, 2024
x – 2y = 3 5x 3y = 2 The lines whose equations are shown intersect at which point?
Given the equations of the two lines, ( x - 2y = 3 ) and ( 5x + 3y = 2 ), at which point do these lines intersect?
4 Answers
x= 2y+3
and 5x=2 – 3y —> x=2- 3y/5
You say x=x
2y+3 = 2 – 3y/5
you get 10y+3y= -15+2
13y=-13
y=-1
You substitute y in the equation x= 2y+3 to get x=2(-1) + 3
x= 1
so the point of intersection is (1,-1)
x – 2y = 3
5x + 3y = 3
3x – 6y = 9
10x + 6y = 6
13x = 15
x = 15/13
15/13 – 2y = 3
2y = 15/13 – 3
2y = 15/13 – 39/13
2y = -24/13
y = -12/13
So, the lines intersect at point (15/13, -12/13).
Jan 08, 2025
On factorising the two expressions, it extremely is (x – 2) (x – 3) __________ (x + 5) (x – 3) the elementary aspects cancel out leaving, (x – 2) _____ (x + 5) As for the 2d questions, it ought to help to rephrase to be clearer.
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