Respuesta :
Answer:
The solutions for the system of equations are (0, 12) and (3, 3).
Step-by-step explanation:
To solve the system algebraically, we can set the two equations equal to each other since they both equal y:
2x^2 - 9x + 12 = -3x + 12
Next, we can combine like terms and set the equation to zero:
2x^2 - 6x = 0
Now, we can factor out the common term x:
2x(x - 3) = 0
Setting each factor equal to zero gives us the solutions for x:
2x = 0 --> x = 0
x - 3 = 0 --> x = 3
So, the solutions for x are x = 0 and x = 3.
Now, we can substitute these values back into one of the original equations to solve for y. Using the second equation y = -3x + 12, we get:
When x = 0:
y = -3(0) + 12
y = 12
When x = 3:
y = -3(3) + 12
y = -9 + 12
y = 3
Therefore, the solutions for the system of equations are (0, 12) and (3, 3).
This solution makes sense because when we graph the two equations, we can see that they intersect at the points (0, 12) and (3, 3), confirming our algebraic solution.
