how do i solve multi step equations

Question

i need to find the solution for y= 2x-1 and 3x-y=-1

Answer 1

I assume you are asking for the solution of the system. Then, the solution is the (x, y) pair that is a solution to BOTH equations. Hence, the y value is the same at that point. Let's solve each equation for y:

 

y = 2x - 1 and y = 3x + 1

 

Since the y values are the same in each case, by substitution

 

2x - 1 = 3x + 1

 

Then, subtracting 2x and 1 from each side, we have

 

-2 = x.

 

Substituting this value of x, we get y = 2(-2) - 1 and y = 3(-2) + 1. This yields y = -5 in each case.

 

Let's check.

 

2(-2) - 1 = -4 - 1 = -5 and 3(-2) + 1 = -6 + 1 = -5

Answer 2

Hey Stephanie -- here's another angle ... 1= 2x-y and -1= 3x-y ==> having another x drops us 2: x= -2 ... thus y= 2(-2) -1 = -5 ... (-2,-5) intersection ... Regards, ma'am :)

Answer 3

y = 2x-1 ......(1)

Solving for y from 3x-y = -1 leads to,

y = 3x+1 ......(2)

Substituting (1) into (2)

2x-1 = 3x+1

So,

x = -2, y = 2x-1 = -2*2-1 = -5

 

Answer: (-2, -5)

Answer 4

Since one equation is already solved for "y", we can use substitution method.

y = 2x − 1
3x − y = − 1

In second equation let's replace "y" by "2x - 1"

3x - (2x - 1) = - 1

3x - 2x + 1 = - 1

 x + 1 = - 1
     - 1    - 1

x = - 2

Now, in first equation, let's replace "x" by "- 2"

y = 2*(- 2) - 1

y = - 5

The answer is the pair of numbers (-2, -5)

Let's verify the answer:

1. -5 = 2*(-2) - 1
    -5 = -5

2.  3*(-2) - (-5) = - 1
       -6 + 5 = -1
       -1 = -1