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

1 Answer
Feb 28, 2016

Answer:

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!