divide the first equation by -3.
Aren't they the same line?
-27x - 18y = -180
9x + 6y = 60
Aren't they the same line?
a+8b=11
3x+2y=-17
First, let's choose one equation and multiply it by a constant to make the coefficients of x or y equal. Let's multiply the second equation by -3:
-3(9x + 6y) = -3(60)
-27x - 18y = -180
Now, we can add the equations together to eliminate the x variable:
-27x - 18y + (-27x - 18y) = -180 + (-180)
-54x - 36y = -360
Simplifying the equation, we have:
-54x - 36y = -360
Now, let's see if this equation is equivalent to the original first equation. We can divide both sides by -9 to check:
(-54x)/(-9) - (36y)/(-9) = -360/(-9)
6x + 4y = 40
As we can see, -54x - 36y = -360 simplifies to 6x + 4y = 40, which is exactly the same as the original second equation. This means that the two equations are equivalent and represent the same line.
Since there is no unique solution and the two equations represent the same line, the system has infinitely many solutions.