How do you find the intersection of two lines algebraically?

Answer 1

first write both equations in the slope-intercept form:

y = mx + b.

then rewrite them in standand form:

ax + by = c.

solve for one variable, x or y, subtitute solved value to get second amount, there is you solution set to the system.

Answer 2

This is solved by working out where the (x,y) co-ordinates are the same in both lines. This can be solved using simultaneous equations.

e.g.

y = 4x + 1 (i)
2y = -2x + 3 (ii)

In this case, you want to make the two y values equal, so double (i)

2y = 8x + 2
2y = -2x

These are now equal, so

-2x = 8x + 2
-10x = 2
x = -1/5

Now we can plug this x co-ordinate in to find the corresponding y co-ordinate

y = 4x + 1
x = -1/5

y = 4(-1/5) + 1
y = 1/5

Therefore the two lines intersect at (-1/5,1/5)

Answer 3

if you are given the equations of the line, then u can solve for the values of x and y, which are the coordinates of the points of intersection of the lines

this is my favorite part of the mathematics.. algebra and geometry are somewhat shown to be related ..just as all the math

Answer 4

Write the two equations for the lines in the form
α1x + ß1y = k1
α2x + ß2y = k2
and then solve them simultaneously.

HTH

Doug

Answer 5

solve these two equations for two variables. zero solution will be point of intersection. If no real solution, lines dont intersect.

Answer 6

just solve the two eqns. and the value of x & y will be the intersection point eg. if x=2 & y=3 the intersection point will be (2,3)

Answer 7

you need to find the linear equation for both the lines.
your equation will appear in the following form.
Ax+By = C
Dx+Ey = F

Solve those equation for x and y value, (x,y) will be the point of intersection.