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Answer 1

Yet another system of equations problem (many appear on Ask an Expert). This one is non-linear (exponents).

(1) x² + y² = 5

(2) x - 3y = 5

Can do by substitution x = 5 + 3y

(5 + 3y)² + y² = 5 Use FOIL to expand

25 + 30y + 9y² + y² = 5 Combine terms, set = 0

10y² + 30y + 20 = 0 Divide by 10

y² + 3y + 2 = 0 Factor

(y + 1)(y + 2) = 0, So y = -1 or -2. Substitute in (2) to find related x value.

Answers: {x = -1; y = -2} {x = 2; y = -1)

Check on Desmos Graphing Calculator (it's a circle intersected by a straight line in two places).

Answer 2

Since x - 3y = 5, x = 3y+5.

So, (3y + 5)² + y² = 5

9y² + 30y + 25 + y² = 5

10y² + 30y + 20 = 0

y² + 3y + 2 = 0

(y + 2)(y + 1) = 0

y = -1 or -2

If y = -1, then x = 3(-1) + 5 = 2

If y = -2, then x = 3(-2) + 5 = -1

Solutions: (2,-1) and (-1,-2)