To solve the system of equations given by:
1. y = x² – 5x + 4
2. y = x² – 9x + 18
We can set the equations equal to each other since both expressions are equal to y.
x² – 5x + 4 = x² – 9x + 18
Next, we can eliminate x² from both sides:
-5x + 4 = -9x + 18
Now, rearranging the equation gives:
9x – 5x = 18 – 4
4x = 14
Dividing both sides by 4:
x = 3.5
Now that we have x, we can substitute it back into one of the original equations to find y. Let’s use the first equation:
y = (3.5)² – 5(3.5) + 4
y = 12.25 – 17.5 + 4
y = -1.25
Thus, the solution to the system of equations is:
(x, y) = (3.5, -1.25)