Solve the system of equtions and check your answer. 2x - y + 1 = 0 x + 2y - 6 = 0
3 Answers
justaguide | College Teacher | (Level 2) Distinguished Educator
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
malkaam | Student, Undergraduate | (Level 1) Valedictorian
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.
tonys538 | Student, Undergraduate | (Level 1) Valedictorian
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