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

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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**

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.

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