x² + y² = 10

y = x + 2

x² + (x + 2)² = 10 {substituted (x + 2), in for y, into top equation}

x² + (x + 2)(x + 2) = 10 {when squaring a binomial, multiply it by itself}

x² + x² + 4x + 4 = 10 {used foil method}

2x² + 4x + 4 = 10 {combined like terms}

2x² + 4x - 6 = 0 {subtracted 10 from both sides}

2(x² + 2x - 3) = 0 {factored 2 out}

2(x + 3)(x - 1) = 0 {factored into two binomials}

x + 3 = 0 or x - 1 = 0 {set each factor equal to 0, excluding 2}

**x = -3 or x = 1 **{solved each equation for x}

y = x + 2

y = -3 + 2 or y = 1 + 2 {substituted -3 and 1 in for y}

**y = -1 or y = 3** {solved each equation for y}

Solutions are (-3,-1) or (1,3)

*- Algebra House*
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