Question

How do you solve the system 2x = y + 1 and 2x - y = 5?

Answer 1

You can either solve by elimination or by substitution. I'll solve by substitution

Explanation:

To perform substitution, you must first isolate one of the variables in one of the equations.

It would be easiest to isolate y in the first equation.

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

Knowing y, we can substitute the value of y (2x - 1) for y in the other equation.

`2x - (2x - 1) = 5`

`2x - 2x + 1 = 5`

`0x = 4`

`x = 4/0`

`x = O/`, since division by 0 is undefined in mathematics.

The solution set is `{O/}`.

You could also have seen that there would be no solution by isolating y in both the original equations.

`2x - 1 = y, 2x - 5 = y`

As you can see, in both equations x is multiplied by 2, giving the same number as a result. However, in the first equation this value is subtracted by 1 while in the second it is subtracted by 5. This suggests two values of y for one value of x, which is impossible. So, at this point we can conclude that the lines are parallel and so they never intersect (in a systems of equations, the point of intersection of two lines is the solution).

If you have learned about linear functions, you should know that in slope intercept form, `y = mx + b`, the value of m is the same but the value of b is different when comparing the equations of lines that are parallel.

Hello from Esquimalt!

Hopefully this helps!