Solve the system of equtions and check your answer. 2x - y + 1 = 0 x + 2y - 6 = 0

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The system of equations

2x - y + 1 = 0 ...(1)

x + 2y - 6 = 0 ...(2)

has to be solved.

(1) - 2*(2)

=> 2x - 2x - y - 4y + 1 + 12 = 0

=> -5y = -13

=> y = 13/5

x = 6 - 2y = 6 - 26/5 = 4/5

To check the solution, substitute x and y in the equations and check the result.

2x - y + 1 = 2*(4/5) - (13/5) + 1 = 0

x + 2y - 6 = 4/5 + 26/5 - 6 = 0

The solution of the given system of equations is x = 4/5 and y = 13/5

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malkaam | Student, Undergraduate | (Level 1) Valedictorian

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You can solve this with the method of substitution,

2x - y + 1 = 0  ------(i)

x + 2y - 6 = 0  ------(ii)

Consider eq(ii) and isolate x

x + 2y = 6

x = 6 - 2y

Insert the value of x in eq(ii)

2x - y + 1 = 0

2(6 - 2y) - y + 1 = 0

12 - 4y - y + 1 = 0

13 - 5y = 0 

13 - 5y - 13 = 0 - 13    Subtract 13 from both sides

-5y = -13

-5y/-5 = -13/-5           Divide both sides by -5

 y = 13/5

Insert the value of y in eq(ii)

x + 2y - 6 = 0

x + 2(13/5) - 6 = 0

x + 26/5 - 6 = 0

x + 26-30/5 = 0

x - 4/5 = 0

x = 4/5

To verify the answer plug in both the value in any equation and check if both sides are equal, if yes then the answer is correct.

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tonys538 | Student, Undergraduate | (Level 1) Valedictorian

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Another way of solving the equations

2x - y + 1 = 0

x + 2y - 6 = 0

is first expressing y in terms of x using the first equation and then substituting that for y in the second equation.

2x - y + 1 = 0

y = 2x + 1

Put this in the equation x + 2y - 6 = 0

x + 2*(2x + 1) - 6 = 0

x + 4x + 2 - 6 = 0

5x = 4

x = 4/5

y = 2x + 1 = 8/5 + 1 = 13/5

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