Question

Solve the system of equations by substitution. What is the solution for x?

2x + y = 1
4x + 2y = −2

Answer 1

??

Answer 2

Specifically by substitution? ok then...
The first step is to take one equation, and isolate either x or y, let's use y, and the first equation.

2x + y =1, this means that
y = 1 - 2x
We now have an alternate value for y IN TERMS OF x. Let us therefore SUBSTITUTE this value for the y in the SECOND equation.
4x + 2y = -2, substituting gives us...
4x + 2(1 - 2x) = -2
4x + 2 - 4x = -2
2 = -2, which means there is no solution for x, since 2 is never equal to -2

Answer 3

That make sense, if you graph these two lines in the Cartesian plane, you'll see they are parallel, and therefore, do not intersect at any point, thus there is no solution.

Answer 4

thank you what about this question
−2x + y = 1
−4x + y = −1

Answer 5

It appears that once again, it is easier to isolate y... Let's take the first equation.
-2x + y = 1, therefore
y = 2x + 1, we'll stop here, and go to the second equation...

-4x + y = -1, we use the value for y we acquired in the first equation and substitute it to the y here...
-4x + (2x + 1) = -1
-2x + 1 = -1
-2x = -2
x = 1.

Answer 6

If I was mistaken, or wasn't clear, please tell me.

Answer 7

my options were A- 3,1
B- -1,3
c- -1,-3
D - 1,3

Answer 8

What's D?

Answer 9

if D is 1, 3, then D is correct. Do you wish me to show you why?

Answer 10

yes please

Answer 11

so, we found out that x = 1, right? so all that remains is to substitute 1 for x in any of the two given equations... Let's choose the second.
-4x + y = -1, substituting 1 for x, we get...
-4(1) + y = -1
-4 + y = -1
y = -1 + 4
y = 3.
Since we already know that x = 1, with y = 3, the answer is 1,3

If you wish me to explain some parts, tell me :)