Math equationsFind a common solution to the two equations y = 2-x and y = 2x-1

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The equations to be solved for x and y are y = 2 - x and y = 2x - 1

Equate y from the two equations.

2 - x = 2x - 1

=> 3x = 3

=> x = 1

y = 2 - x = 2 - 1 = 1

The solution of the equations is x = 1 and y = 1

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tonys538 | Student, Undergraduate | (Level 1) Valedictorian

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The system of equations y = 2-x and y = 2x-1 has to be solved.

y = 2-x ...(1)

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

(1) - (2)

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

0 = 2 - x - 2x + 1

-3x + 3 = 0

x = 1

2*(1) + (2)

2y + y = 4 - 2x + 2x - 1

3y = 3

y = 1

The solution of the given system of equations is x = 1 and y = 1

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

To determine the common solution, we'll equate both expressions of the lines:
2 - x = 2x - 1
We'll add x both sides:
2 = 3x - 1
We'll add 1 both sides:
3x = 3
x = 1
y = 2 - 1 => y = 1
The common solution of the equation is represented by the point that lies on the 1st bisectrix: (1 , 1).

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