Practise substituting a linear equation into a quadratic relation, solving the resulting quadratic and pairing both coordinates for every valid intersection.
Find the coordinates of the points of intersection of the curve and the line with equations
2(2−y−4)y+5y2=24
or 2(2y24−5y2)+y+4[=0]
or 2 x(-4-2 x)+5(-4-2 x)^2=24
*M1
OE
For eliminating x or y. Condone sign errors in the rearrangements.
4 y^2-4 y=24 or 16 x^2+72 x+56[=0]
DM1
OE
For simplifying to a 3-term quadratic;
terms do not all have to be on the same side.
Condone sign errors in the expansions or in the collecting of terms.
y=-2, y=3 or x=-1, x=-7/2
B1
OE
Not for a correct (x, y) pair. Allow from a correct quadratic (ignore any working seen).
(-1,-2),(-7/2, 3)
B1
OE
Allow from a correct quadratic (ignore any working seen).
Condone x=-1 and y=-2 and x=-7/2 and y=3.