x+y-1=2(y-x) y=3x-1

Question

substitution method

x+y-1=2(y-x)

y=3x-1

Answer 1

When solving a system of equations in 2 varibles by substitution, solve one of the equations for x or y and then sustitute that value into the other equation. In your example: x + y = 2(y - x) and y = 3x - 1 The second equation is already solved for y. We can now substitute 3x - 1 for y in the other equation. x + (3x -1)- 1 = 2((3x - 1) - x) Now we can simplify and solve for x. 4x - 2 = 2(2x - 1) 4x - 2 = 4x - 2 Notice that the two sides are exactly the same? This indicates that the solution set is the set of all real numbers. If the equation had simplified to a false statement like 3 = 4, then there would be no solutions. If the equation had simplified to something like x = 2, then you would substitute the 2 for x in either of the original equations to solve for y.