Question

I need a little help with:
Solve the system of equations by substitution. What is the solution for x?
2x + y = 1
4x + 2y = −2

Answer 1

my attempt
2x + y = 1
4x + 2y = −2

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

4x + 2y = −2
4x + 2(1-2x) = −2
4x + 2 -4x=-2
x +2=-2
-2 -2
____________
x=-4
2(-4) + y = 1
-8+y=1
+8 +8
_____________
y = 7 x=-4
______________
checking
2(-4)+ 7 = 1
-8+7=1
-1=1

4x + 2y = −2
4(-4) + 2(7) = −2
-16 + 14 =-2
-2=-2

Answer 2

This system of equations has no solution and is graphically a pair of parallel lines.

Answer 3

Your attempt was going well up until your 9th line. At that point, the x terms completely disappear.

Answer 4

Another way to see that you have parallel lines is to put the equations into slope-intercept form. There you would see that you have 2 equations of the form:

y=mx+b

where the "m" values are the same but the "b" s are different.

Answer 5

inst 4+-4 =0 so nothing goes by the x?

Answer 6

y = -2x + 1 and

y = -2x - 1

Answer 7

2x + y = 1 => y = 1-2x
4x + 2y = -2

4x + 2 (1 -2x) = -2
4x + 2 - 4x = -2
2= -2

Answer 8

Actually, your 9th line is not:

x +2=-2

It instead becomes the incongruous:

2 = -2

which cannot be, which shows parallel lines. It is an "inconsistent" system.

Answer 9

Hopefully, your homework assignment contains at least a couple of more sets of equations, some pairs of which that can be solved, but this set definitely cannot be solved.

Answer 10

You see, in your 8th line, you have 4x and -4x on the left side. They cancel and you are left with no "x" terms.

Answer 11

So, your 9th line is not:

x +2=-2

Instead, it is :

2 = -2

And that's where you can stop. You don't have to go further.

Answer 12

When you are trying to solve a pair of x,y equations, you are going to get one of 3 situations to occur:

1) they intersect in one point (independent system)

2) they are parallel (inconsistent system)

3) they are actually the same line (dependent system)

Here, you have #2, an inconsistent or parallel line system.

Answer 13

Ah I see thank you.
the assessment has the option of no solution
So if 2= -2
I makes it parallel.