Solving Systems using Substitution

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8-2: Solving Systems of Equations using Substitution

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Solving Systems using Substitution

Substitution – Replacing Evaluate one equation for one variable Example: 𝑦=3𝑥+7 Substitute the resulting expression for the variable in the second equation.

Steps to Solving a Sd Kf

Solve the system by using substitution: y = 4x – 1 2x + 2y = 3 Because y = 4x – 1, substitute 4x – 1 for y in 2x + 2y = 3. 2x + 2y = 3  Write the second equation 2x + 2(4x – 1) = 3  Substitute 4x – 1 for y 2x + 8x – 2 = 3  Use the Distributive Property 10x – 2 = 3  Simplify 10x = 5  Add 2 to each side x = ½  Divide each side by 10 Substitute ½ for x in either equation and solve for y. y = 4x – 1 y = 4(½) – 1 y = 2 – 1 y = 1 The solution of the system is (½, 1)

Solve the system by using substitution: -9x + 5y = -1 -3x + y = 4 The solution of the system is (-3.5, -6.5)

Solve the system by using substitution: -2x + y = 3 3x – 2y = 0 The solution of the system is (-6, -9)