how can i find where two lines intersect? i have the equation for both lines.?

Question

the equation for the first line is 4y+x=0
the second is y=2x-3
where will these two lines intersect?

i got (1/3,1/3) which im pretty sure is wrong. could someone please show me how to do this

i know how to graph it i want to know how to work it out

Answer 1

Graphing is a good idea to at least give you a general idea of where they intersect. If they cross at a nice place (some whole number) the graph might even give you the answer. The teacher probably expects you to do it algebraically though. Finding where two lines intersect is the same as solving the system of two equations.
The second equation is already in terms of y. substitute that in the other equation. Then solve for x. After finding x, you can put your value of x in one of the equations then solve for y.
(x,y) will be your answer.

It is a good idea to put your x and y in both equations to double check your answer. if your answer doesn't make one of the equations valid, then you made a mistake somewhere

Answer 2

Where Two Lines Intersect

Answer 3

The two lines intersect where they have the same x and y values. Solve these two equations as a system, and boom, you've got the point where they meet.

First, rearrange one of the equations so that the variables are in the same place in both equations (it makes things easier, trust me). I'll rearrange the second equation to fit the format of the first:

4y + x = 0
y - 2x = -3

Now I need to multiply one of my equations so that one of the variables has the negative coefficient of the same variable in the other equation. For example:

4y + x = 0
-4(y - 2x = -3)

Leads to:

4y + x = 0
-4y + 8x = 12

Now add the two equations, term for term. 4y and -4y will cancel out, leaving only one variable.

9x = 12

x = 12/9 = 4/3

Now that you've got x, plug that value into either of the original equations and solve for y:

y = 2(4/3) - 3 = 8/3 - 3 = -1/3

So your point of intersection is (4/3, -1/3)

Answer 4

try to graph it using the slope formula Y= M (X + b)