Question

How many solutions does the system have
6x + 2 = y
3y – 18x = 12
one solution
two solutions
infinitely many solutions
no solution

Answer 1

Problems regarding linear equations with two unknowns can be solved using Substitution and/or Elimination Method.
For this let's have elimination.
For you to eliminate one variable,
6x + 2 = y -----equation 1
3y - 18x = 12 ----equation 2
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From equation 1:
multiply equation 1 by 3
[6x + 2 = y] x3
18x + 6 = 3y
Transpose 3y to the left and 6 to the right
-3y + 18x = -6 -----equation 1'
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Add equations 1' and 2
-3y + 18x = -6
+ 3y - 18x = 12
0 + 0 is not equal to 6
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When this occurs to the system of equations, this only means that there's no solution since we can't get the values of x and y and that no values of x and y could be true to both equations

Answer 2

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