Solve fr substitution

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Solve fr substitution

x^2+y^2=10
y=x+2
AlgebraHouse AlgebraHouse
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Re: Solve fr substitution

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