How do I solve this system of equations?

Question

x=y-1,
2x=3y

Thank you.

Answer 1

Hah..we just started learning about this.

Ok, so the equation that you want to solve is 2x=3y, right?
Now, you know from the first equation that x=y-1. So now, replace the '2x' and plug in y-1 for x. your equation is now
2(y-1)=3y

Now all your variables are the same so you can get y alone, by moving one of the variable to the other side. But first, get rid of the parenthasis by using the distributive property

2y-2=3y

No move the variables, let's move 2y

2y-2=3y
-2y -2y
NEW EQUATION IS..

-2=1y, or

-2=y.
now you know what y is, so solve for x, using y.

x= -2-1
x= -3
now you know x and y so plug in the numbers to double check

2(-3)=3(-2)
2(-3)=-6
-6= -6

The answer to this problem then is
x= -3
y= -2

Solution = -6

Answer 2

Since you've got the first equation solved for a single variable, plug that value into the second.

2x = 3y
2(y-1) = 3y (substitute y-1 for x)
2y - 2 = 3y (Distribute the 2
-2 = y (subtract 2y from both sides)

Then, plug this value into your first equation:

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

The solution is {-3, -2}

Answer 3

x=y-1
2x=3y
---------------
x=1.5y
-------------
1.5y=y-1
.5y=-1
y=-2
-------------
2x=3(-2)
2x=-6
x=-3
--------------

(-3,-2)