math problem?

Question

the given pairs of lines intersects. Find the point of intersection.

L: x + y = 5
M: 3x - y = 7

can somebody explain how you solve this

Answer 1

I sure can.
Solve the first problem for y.. you will get y=5-x
Since you know this, you can now insert 5-x into the second equation in place of y.

3x-(5-x)=7
3x-5+x=7
4x-5=7
4x=12
x=3

Now that you know x=3, insert it into the first or second equation, whichever..and you will find that y=2.

Hope I helped!

Answer 2

how can 2 lines intersect? there are different possibilities:

1) they don't. such lines are called parallel lines. the lines necessarily have the same slope.

2) the lines coincide. in other words, they're both the same line.

3) the lines intersect at one and only one point. this point satisfies both equations. to find this point when given the equations of the two lines, solve the equations simulataneously. there are several ways to do this.
in the form your example is in, the quickest is to first add the two equations together (add the two left sides together and add the two right sides together to form a new equation, notice that one has a +y and the other has a -y so adding with cancel these and you'll be left with an equation with only x).

4x = 12
x = 12/4 = 3
now you know x, plug it into either L or M (L is the simpler equation so use it) and solve for y:

3+y=5
y=5-3=2
so the point is
(3,2)

Answer 3

first off, u put each line to point-slope formula
Line L would be y=5 - x (substract x from both sides)
Line M would be y = 3x - 7 (subtract 3x then distribute the negative)

to find the point of intersection u have a rule known as f(x)=g(x) for two intersection lines ( set Line L equal to Line M)

5 - x = 3x - 7
4x = 12
x = 3 ( this is the X Coordinate where your lines intersected)
then, plug in that number to Line L to find the y coordinate
y = 5 - 3
y= 2

so ur coordinate of intersection is (3,2)
hope that helped

Answer 4

You're looking for the (x, y) point that will work in both equations.
x + y = 5
3x - y = 7 Add the equations together to get
4x = 12 Then
x = 3 and from the first equation (putting 3 in for x) y = 2 so the point of intersection is (3, 2)

Doug

Answer 5

A solution for x & y will be the point of intersection of these two lines.
. . . . . . . . x + y = 5................(1)
. . . . .. . .3x - y = 7 ...............(2)
(1) + (2).4x = 12
. . . . . . . .x = 12/4 = 3
Substitute the value of x in (1)
. . . . . . . .3 + y = 5
. . . . . . . . . . . y = 5 - 3 = 2
Hence, the point (3,2) is the point of intersection.
=====================================

Answer 6

Put both in slope intercept form.

L: y=-x + 5
M: y=3x-7

Set both equations equal to one another.

-x+5=3x-7

Solve for X to get: 4x=12; x=3.

Plug X into one equation to get the Y value:
L: 3 +y=5
y=2

Plur X into the other equation to check your work:

y=3(3) - 7

y=2.

These two lines intersect at (3,2)

Hope this helps

Answer 7

to find the points where the lines intersect, find the x and y which solve both of these equations.

x+y=5
3x-7=7

x and y are equal at the point of intersection so we can add the equations together

x+y=5
3x-y=7
-----------
4x=12
=>x=3

and we have x+y=5
so 3+y=5 => y=2

So the lines intersect at the point (3, 2)

Answer 8

Set both lines equal to y.

y=5-X

y=3X-7

Then subsititute 5-X or 3X-7 for y since they are equal.

5-X=3X-7

Solve for X.

12=4X
X=3

The X point is 3.
then put 3 in for X in one of the equations and solve for y.

X+Y=5
3+Y=5
Y=2.

Thus the intersection point is (3,2)

Answer 9

You can actually add equations together to come up with a third equation which shares the same solution set.

In this situation, that method gets rid of our y variable. We are left with 4x = 12 or x = 3.

Now, 3 + y = 5 or y = 2.

Answer 10

First: Solve for x (x= 5 - y)
Next: Put y into the other equation [3(5 - y) - y = 7]
You can solve it from there by finding y and then finding x using simple algebra.