#7.

a) 3x + y = 4

x² – 3y = -32

First:

3x + y = 4

y = -3x + 4

Then:

x² – 3y = -32

x² – 3(-3x + 4) = -32

x² + 9x – 12 = -32

x² + 9x + 20 = 0

(x + 5) (x + 4) = 0

x + 5 = 0

x = -5

x + 4 = 0

x = -4

x = -5 AND x = -4

Next:

x² – 3y = -32

y = -3x + 4

y = -3(-5) + 4

y = 15 + 4

y = 19

y = -3x + 4

y = -3(-4) + 4

y = 12 + 4

y = 16

So:

(-5 , 19) ✓ AND (-4 , 16) ✓

Check:

3x + y = 4

x² – 3y = -32

3(-4) + 16 = 4

(-4)² – 3(16) = -32

-12 + 16 = 4

16 – 48 = -32

4 = 4 ✓

-32 = -32 ✓

(-4 , 16) ✓

AND

3x + y = 4

x² – 3y = -32

3(-5) + 19 = 4

(-5)² – 3(19) = -32

-15 + 19 = 4

25 – 57 = -32

4 = 4 ✓

-32 = -32 ✓

(-5 , 19) ✓

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