How do you find the intersection?

Question

of x-y=4 and 2x+y=14. If possible, Can you explain it please instead of just the answer?

Can i just solve for y and then set them equal to each other?

Answer 1

You can solve the equations for x and y or you can graph them.

To solve by substitution; x - y = 4 implies that x = 4 + y
plug into 2nd equation; 2(4+y) +y = 14
8 + 3y = 14
3y = 6
y = 2

plug back into 1st equa. x - 2 = 4
x = 6

therefore the intersect is at y=2, x=6

If you physically graph it the results will be the same

Answer 2

I'm teaching this right now in my Algebra class. There are three ways to find the intersection. By graphing the lines and seeing where they cross, by substitution, or by addition. The easiest for this problem would be addition. First write the problems one on top of the other then you add each part and you should get 3x = 18 since the y values will cancel out. Divide both sides by 3 and you get x = 6. Then you take your 6 and plug it into the first equation where the x is. You change x - y = 4 to 6 - y = 4 and realize y is 2. So we have x = 6 and y = 2. The ordered pair (x,y) is (6,2). That is your point of intersection.

You could also solve the both equations for y and set them equal to each other to find x.

The person who told you the answer is (3,-1) made an error. The answer will not work for the second equation.

Answer 3

equating two given equations will lead in finding there intersection..
for example: x-y=4 and 2x+y=14

solution: x-y=4 will be the same as x=4+y and 2x+y=14 will be x=(14-y)/2 ...then equate both x... deriving the equation, 4+y=(14-y)/2..then get the value of y.. y=2 and substitute y to any given equation and fin x.. the the coordinate will be the solved x, and y.. the answer is (6,2) w/c is the intersection...

Answer 4

This is called a system of equations.

Here is a step by step you can apply to future problems:

1. Solve one of them for x, and the other for y.
2x + y = 14 --> y=14-2x
x - y = 4 --> x=4+y

2. Use one and substitute it into the other to combine like-terms
y=14-2x --> y = 14-2(4+y)
x=4+y --> x = 4+14-2x

3. Solve each of those for x and y
y = 14-2(4+y) --> y+2y=14-8 --> 3y = 6 --> y=2
x = 4+14-2x --> 2x+x = 18 --> 3x = 18 --> x=6

Answer 5

Think of these two equations as a system and that they work together.
Each of these equations has an infinite number of answers, all in the form of ordered pairs. But as a system there is only one answer. It is the ordered pair that works in BOTH of them. There is only one ordered pair that will work in both equations.
You should also know that there are several ways to find this ordered pair. I will show you the easiest way for this system of two equations.

The method I will use is called the addition method

We will first get rid of one of the variables by adding the equations together,

x - y = 4
2x + y = 14
-------------------------
3x+ 0 = 18
So. 3x = 18
x = 6 ( I got this by dividing both sides of this equation by 3

now we need to find y. Use either one of the original equations to do this. I always pick the easy one :-)

x - y = 4
put in 6 for x

6 - y = 4
We need to get y by itself, so:
we first add -6 to both sides
-6 + 6 - y = 4 -6
0 - y = -2
-y = -2
So y = 2 and the ordered pair is ( 6, 2 )

This ordered pair will solve BOTH of these equations and it is the ONLY ordered pair that will work in both equations.
It is called the intersection of the two equations.

Answer 6

Intersection is the point where both will cross. So since you have two equations, it'll be the point that can satisfy both equations. They will have the same x and y value for one point.

First, convert one of the equations into y intercept form, it doesn't matter which one.

So say you take the first one ( x-y = 4)
You should get:
y = x - 4

Now you can substitute in that the value of y into the other equation. In the next equation, replace y with (x-4), because that is what y equals.
2x + 4y = 14

2x + 4(x-4) = 14

Now solve for x.
2x + 4x - 16 = 14
6x = 30
x = 6

You have x = 6. So plug in the value of x into one of the equations and solve for y.
6-y = 4
6 -y = 4
-y = -2
y = 2


(6,2)

To check, plug in y and x back into the equations and see if it works out.

Answer 7

The intersection is the solution to the system of equations.
x - y = 4
2x + y = 14
add the equations :
3x = 18
x = 6

Find y by substituting the value of x into either equation.
2*6 + y = 14
y = 14 - 12
y = 2

The lines inteersect at (6,2)

Answer 8

x-y=4 ... (1)
2x+y=14 ... (2)

From (1), x = 4 + y ..... (3)

Substitute the value of x into (2)

2(4+y) + y = 14
8 + 2y + y = 14
3y = 14 - 8
3y = 6
y = 6/3
y = 3

Substitute this value of y in (3)

x = 4 + 3
x = 7

Answer 9

well the best method is to draw these lines on graph paper
but it theoretically u want then just calculate the value of one of variable frm one equation and substitute it in other
as frm eq. 1
y=x-4
now on substituiting it in second equation we get,
2x+ x-4=14
3x= 18
x=18/3
x=6
so y =6-4=2
so the point of intersection is (6,2)
u can also check it by putting the values in two equatins and they will justify it

Answer 10

The easiest way to find an intersection is to go to the corner....