Start by solving one equation for one variable in terms of the other variable. We can solve the first equation for x:
2x + 3y = 4
Subtract 3y from both sides:
2x = 4 - 3y
Divide both sides by 2:
x = 2 - (3/2)y
Now substitute this expression for x into the second equation:
-4(2 - (3/2)y) - 6y = -8
Distribute:
-8 + 6y - 6y = -8
Combine like terms:
-8 = -8
The equation -8 = -8 is a true statement, indicating that the original equations are dependent and infinitely many solutions exist. This means that any values of x and y that satisfy one of the equations will also satisfy the other equation.
Use the substitution method to solve the system 2x + 3y=4-4x -6y=-8.
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