The line y=5-x intersects the curve y=x^2-3x+2 at the points P and Q. Find the (x,y) coordinates of P and Q.
Step 1: To find the points of intersection, we must find where the y and x values are equal. Therefore 5-x=x2-3x+2 where the y-values are equal.
Step 2: Rearrange the above into the quadratic equation x2-2x-3=0 by adding -x and subtracting 5 from both sides.
Step 3: Factorise the equation to find the x-values where the lines intersect. This gives (x+1)(x-3)=0.
Step 4: This shows that x+1=0 and x-3=0, therefore x=-1 or 3.
Step 5: Find the y-values that correspond to the above x-values. When x=-1, y=5-(-1)=6 and when x=3, y=5-3=2. Therefore P and Q are the points (-1,6) and (3,2)
