4x−6y=12 −2x+3y=−6

Question
Systems of equations
asked 2020-11-08
4x−6y=12
−2x+3y=−6

Answers (1)

2020-11-09
Notice that you can divide the first equation by 2 to simplify the system: 2x-3y=6
-2x+3y=-6
Add the first equation to the second to get the following system:
2x-3y=12
0=0
Therefore, this system reduces to the equation 2x-3y=12
Since we have 1 equation and 2 unknowns, we put y=t (we designate it as a parameter of this system), and get
\(\displaystyle{2}{x}-{3}{t}={12}\to{2}{x}={3}{t}+{12}\to{x}={1.5}{t}+{6}\)
Therefore, the solution is
x=1.5t+6, y=t, t is a parameter.
0

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