How do i solve this similtaneous equation? 5x+y=13 x+y=5?

5x+y=13
- x(-)y=-5 change the + sign to - sign so y will be canceled
---------------
4x =8
x=2

5x+y=13 plug in x=2 to 5x+y=13
5(2)+y=13
10+y=13
y=13-10
y=3 {2,3} answer @(^_^)@

1st & 2nd equations (y):
5x + y = 13
y = 13 - 5x

x + y = 5
y = 5 - x

Solve for x:
13 - 5x = 5 - x
4x = 8
x = 2

Solve for y:
= 13 - 5(2)
= 13 - 10
= 3

Answer: x = 2, y = 3

Proof (1st & 2nd equations):
(5[2] + 3) + (2 + 3) = 13 + 5
(10 + 3) + 5 = 18
13 + 5 = 18
18 = 18

First, rewrite the equation by solving for y.
5x + y = 13 Write the equation.
5x - 5x + y = 13 - 5x Subtract 5x from each side.
y = 13 - 5x Simplify.
Choose four x values and substitute them into y = 13 - 5x.
x y = 13 - 5x y (x, y)
0 y = 13 - 5(0) 13 (0, 13)
1 y = 13 - 5(1) 8 (1, 8)
2 y = 13 - 5(2) 3 (2, 3)
3 y = 13 - 5(3) -2 (3, -2)
Four solutions are (0, 13), (1, 8), (2, 3), and (3, -2).
Example 3 Graph a Linear Equation
Graph y = -x + 3 by plotting ordered pairs.
First, find ordered pair solutions.
x y = -x + 3 y (x, y)
-1 y = -(-1) + 3 4 (-1, 4)
0 y = -(0) + 3 3 (0, 3)
1 y = -(1) + 3 2 (1, 2)
2 y = -(2) + 3 1 (2, 1)
Four solutions are (-1, 4), (0, 3), (1, 2), and
(2, 1). Plot these ordered pairs and draw a
line through them. Note that the ordered
pair for any point on this line is a solution of
y = -x + 3. The line is a complete graph of
the function.

CHECK It appears from the graph that (4, -1) is also a solution. Check this by
substitution.
y = -x + 3 Write the equation.
-1
?=
–(4) + 3 Replace x with 4 and y with –1.
-1 = -1
Simplify.




you can also do that to the second one

5x+y=13 , rearrange equation to y=13-5x

x+y=5
but y=13-5x, so x+(13-5x)=5
>> 4x=8, x=2

>>y=13-5(2), y=3

>> x=2, y=3

5x+y=13 and x+y=5
x+y = 5 <=> x =5-y. So 5x + y = 5(5-y) + y = 13 <=>
<=> 25 - 5y + y = 13 <=> 4y = 25-13 <=> y = 3 return to
x+y = 5 we have x+3 = 5, so x=2.
x = 2;
y = 3'

The easy way to do it is subtract one from the other since you have a single y term in both

5x + y = 13 - x + y = 5

combine to be

5x - x + y - y = 13 - 5
4x = 8
x = 2

Now just sub this into one of the equations and solve for y

x + y = 5
2 + y = 5
y = 5 - 2
y = 3

That's it

5x + y =13 (let this be equation 1)
x + y =5 (let this be equation 2)
subtracting equation 2 from equation 1,
4x=8
therefore, x =2
substituting the value for x=2 in equation 2,
2 + y = 5
y = 3
The final solution is x=2 , y=3

initiate by factoring out an x x(x^2+5x-6)=0 then element (x^2+5x-6) to (x+6)(x-a million) so x(x+6)(x-a million)=0 set anytime period =0 x=0 x+6=0 x-a million=0 then remedy for x x=0 x=-6 x=a million and those very last 3 numbers are your answer!

Hello ,

You here have two variables & two equations , so solve them together and you will have your answer very fast :

5x + y = 13 ----> (1)
x + y = 5 -----> (2)

by multipling (2) x (-1) and adding them together :

5x + y = 13
-x - y = -5
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.'. 4x = 8 ------->> X = 2

substitute in (1) or (2) with x=2

.'. y= 5 -2 = 3

Answer is : X=2 & Y=3

Note that if the number of variables is more than the number of equation , you won't be able to find the variabbles as an example:

4X - 2Y + 3Z = 8
23X + 14 Y + 5Z = 13

here you can't solve them..

By the way note that the values you get for X & Y are the points where the two functions are met, example

let F(x) = 13 - 5x & G(x) = 5 - x

then if you wrote the graph of the two functions together they will meet at the point ( 2 ,3 ) which is the solution..

Have nice time and ask again if you need anything

You have two options. I prefer substitution, but I will show you both ways.

Substitution:
x+y=5
x=-y+5

5x+y=13
5(-y+5)+y=13
-5y+25+y=13
-4y+25=13
-4y=-12
y=3

Then, plug it in.

x+(3)=5
x+2

Add/Subtract:
First, make the coeffecients of one variable be opposites on each equation.
5x+y=13
x+y=5 (multiply all by -5) -5x-5y=-15

So the 2 equations are
5x+y=13 and
-5x-5y=-25

Then, add them together! The x's cancel out, the y's add up to form a -4y, and the constants add to make -12.
-4y=-12
y=3

Then, plug it in.

x+(3)=5
x+2

Pick the method that is best for you.