Question

Solve the given system algebraically. Show and explain workY+2x=2Y+2=2x

Answer 1

To answer this question, we can proceed as follows:

1. We can show the equations together as follows:

We can rearrange the second equation as follows:

1. Subtract 2x from both sides of the equation:

$y+2=2x\Rightarrow y-2x+2=2x-2x\Rightarrow y-2x+2=0$

2. Subtract 2 from both sides of the equation:

$y-2x+2-2=0-2\Rightarrow y-2x=-2$

And now, we end up with the following system of equations:

We add the two equations, and then we solve for y. Now we have that the value for y = 0. If we substitute this value in either given equation, we can find the value of x as follows:

$y+2x=2\Rightarrow y=0\Rightarrow0+2x=2\Rightarrow\frac{2x}{2}=\frac{2}{2}\Rightarrow x=1$

And now we have that the solution for x is 1 ( x = 1).

Therefore, the solutions for the given system is x = 1, and y = 0 or (x = 1, y = 0).

[We can double-check the result using the two given equations:

First equation

$0+2(1)=2\Rightarrow2=2$

Second equation

$0+2=2(1)\Rightarrow2=2$

In both cases, the results are True. We have checked the result.]