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

1 Answer
Feb 28, 2016

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


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!