Question

The equations -6x + 3y = 6 and x² + y = 10 intersect at the

Answer 1

The values of the letters in coordinates (a, b) and (c,d) are;

a = -4

b = -6

c = 2

d = 6

We are given two equations;

-6x + 3y = 6  ---(eq 1)

x² + y = 10 ---(eq 2)

• We are told that they intersect at coordinates; (a, b) and (c, d).

Let us make y the subject in eq 2 to get;

y = 10 - x²  --(eq 3)

• Let us put 10 - x² into eq 1 to get;

-6x + 3(10 - x²) = 6

expanding further gives;

-6x + 30 - 3x² = 6

rearranging gives;

3x² + 6x - 24 = 0

Using online quadratic equation solver, we have;

x = -4 and x = 2

Putting x = -4 into eq 3 gives;

y = 10 - (-4)²

y = 10 - 16

y = -6

Putting x = 2 into eq 3 gives;

y = 10 - (2)²

y = 10 - 4

y = 6

• Thus, the coordinates are; (-4, -6) and (2, 6)

Comparing with (a, b) and (c,d), we have;

a = -4

b = -6

c = 2

d = 6

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