If the system of equations given below is solved using the substitution method, what is the equation that resu

Question

If the system of equations given below is solved using the substitution method, what is the equation that results from solving the second equation for y, and substituting into the first equation?
3x - 2y = 7

x - y = 5

Answer 1

From second equation.......
x-y=5
=>y=(x-5).............now putting this in first equation

3x-2y=7
=>3x-2(x-5)=7...........this is the equation
=>3x-2x+10=7
=>x+10=7
=>x=-3

and hence y=(x-5)=-3-5=-8

x=-3
y=-8

Answer 2

To solve by the substituion method, first isolate the variable that's easiest to isolate, then plug this into the other equation.

Here, it's easier to isolate a variable from the secon equation than from the first, x would be easiest to pull out but y wouldn't be that much more work. You'd do this:
x - y = 5 add y to each side and get
x = 5 + y ... see, it's easier to isolate the x, but let's get the y...
subtract 5 from each side and get
x-5 = y
Next, substitute the expression for y, that is, (x-5), in place of the y in the first equation:
3x - 2(x-5) = 7
Distribute out the -2 and simplify
3x - 2x + 10 = 7 so x + 10 = 7
Subtract 10 from each side and you get x = -3
Since x - 5 = y, -3 - 5 = y so y = -8
Check by seeing if these numbers work in the first equation
3(-3) - 2(-8) = 7
-9 - (-16) = 7
-9 + 16 = 7
7 = 7
So your solution is (x,y) = (-3, -8)

Answer 3

Use the second equation to solve for y (like the problem says):

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

Now use this in the first equation:
3x - 2y = 7
3x - 2(x - 5) = 7

Simply that to get:
3x - 2x + 10 = 7
x = 7 - 10
x = -3

Answer 4

3x - 2y = 7
x - y = 5

First things first, let's solve the second equation for y.

x - y = 5
y = x - 5

Now, let's plug this into the first equation.
3x - 2y = 7
3x - 2(x - 5) = 7
3x - 2x + 10 = 7
3x - 2x = -3
x = -3