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

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

Question

Solve the system of equations by substitution. What is the solution for x?

2x + y = 1
4x + 2y = -2

whpalmer4 · Answer

Okay, looking at the first equation, you could rearrange that to give y in terms of x very easily, just subtract 2x from both sides.  Now rewrite the second equation, except when you see y, instead substitute the expression you got for y.  Solve for x.  Use the value of x you find to find y with the rearranged first equation.

anonymous · Answer

but what do i subtract 2 to which sides

anonymous · Answer

okay well i got X=0 is the rigth..??

whpalmer4 · Answer

$$2x + y = 1$$ Subtract 2x from both sides to get y alone on the left
$$2x + y - 2x = 1 - 2x$$$$y = 1-2x$$
Now rewrite the second equation with that:
$$4x+2y = -2$$$$4x + 2(1-2x) = -2$$$$4x + 2 - 4x = -2$$$$0x = -4$$
If x = 0, then y = 1-2(0) = 1.  But let's try those values in our equations to check them:
2(0) + 1 = 1 so far so good
4(0) + 2(1) = -2  uh oh, 2 doesn't equal -2.  There's no solution.  If you graph both lines, you'll see that they are parallel.  The solution would be a point where they cross, and parallel lines never cross, so there is no solution to this system of equations.

anonymous · Answer

okay so their is no X VALUE AS THERE IS NO solution right

whpalmer4 · Answer

"there is no x value as there is no solution'

"there is no way they're going to enjoy their English homework" :-)