# 4x−6y=12 −2x+3y=−6

Question
Systems of equations
4x−6y=12
−2x+3y=−6

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.

### Relevant Questions

2x+3y=1
−2x+3y=−7
Solve {(x,+,3y,=,8),(2y,=,x,+,6):}
Solve {(2x,+,3y,=,-1),(6x,+,3y,=,-9):}
Solve the system: {(-2x,+,y,=,5),(-6x,+,3y,=,21):}
Solve the system: {(-3x,+,y,=,2),(9x,-,3y,=,-6):}
2x + 3y = 34
y = 5x
$$\displaystyle{x}–{y}={3}$$
$$\displaystyle{2}{x}+{3}{y}={1}$$
Solve the matrix equation: $$4[2x,y,3z]+3[2,−4,6]=[20,−4,54]$$