Simultaneous Equations- Using the either the method Elimination, or Substitution? urgent

a. y=2X+5
5X-y=1

The answer is x=2, y=9
but how do you do it???

y = 2x + 5
5x - y = 1

substitution

we know y = 2x + 5 so sub it into 2nd equation and solve for x

5x - (2x + 5) = 1
5x - 2x - 5 = 1
3x = 6
x = 2

we now know x = 2 so sub it for x in one of the original equations and solve for y. let's choose equation 2

5(2) - y= 1
10 - y = 1
- y = - 9
y = 9 so (2,9)

elimation

y = 2x + 5
5x - y = 1

- 2x + y = 5
5x - y = 1

add equations

3x = 6
x = 2

we now know x = 2 sub it one of the original equations and solve for y. let's choose equation 1.

y = 2(2) + 5
y = 4 + 5
y = 9

so (2,9)

y = 2x + 5

and

5x - y = 1

since the first equation is already solved for " y," simply use substitution...

5x - (2x + 5) = 1

3x - 5 = 1

3x = 6

x = 2

you can easily find y...check the answers in both equations...you need to !

id est

[x = 2, y = 9]

equation 1: y=2x+5

equation 2: 5x-y=1

substitute y=2x+5 into equation 2...

so 5x-(2x+5)=1

5x-2x-5=1

add 5 to each side of equation...

5x-2x=6

3x=6

divide both sides by 3...

x=2

Now substitute x=2 into equation 1..

y=2*2 + 5

so y=9

answer is x=2, y=9

Substitute y = 2x+5 into 5x-y = 1
so 5x - (2x+5) = 1
5x - 2x - 5 = 1
3x = 1 + 5
3x = 6
x = 2
Then substitute this value of x into y = 2x +5
y = 2(2) + 5
y = 4 +5
y = 9

they made it easy for you see how the first is " y=2x+5" plug that into "5x-y=1"
so 5x-(2x+5)=1
5x-2x-5=1
3x=6
x=2

plugging 2 into " y=2x+5" you get
y=2(2)+5
y=9