#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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