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how do i solve multi step equations

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

Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
4.6 4.6 (13 lesson ratings) (13)
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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

can i get a little more detail please.?
Mark R. | Experienced, Knowledgeable, and Patient, Moss League Math TutorExperienced, Knowledgeable, and Patient,...
5.0 5.0 (2 lesson ratings) (2)
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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
4.9 4.9 (219 lesson ratings) (219)
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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 :)
Nataliya D. | Patient and effective tutor for your most difficult subject.Patient and effective tutor for your mos...
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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)