How do you solve the system 2x = y + 1 and 2x - y = 5?
1 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.
Knowing y, we can substitute the value of y (2x - 1) for y in the other equation.
The solution set is
You could also have seen that there would be no solution by isolating y in both the original equations.
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,
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Hopefully this helps!