9.1 - Solving Systems of Equations by Substitution

Solve using substitution. y = -3x y - x = 24

Answer.) y - x = 24 = -3x - x = 24 --> -4x = 24 = x = -6 y = -3x = y = -3(-6) = y = 18

Solve using substitution. 2 + y = 3x 6x - 5y = 8

Answer.) 2 + y = 3x --> y = 3x - 2 = 6x - 5y = 8 = 6x - 5(3x - 2) = 8 --> 6x - 15x +10 = 8 = -9x = 8 - 10 --> -9x = -2 --> x = 2/9 2 + y = 3x = 2 + y = 3(2/9) --> 2 + y = 2/3 = y = 2/3 - 2 --> y = -4/3

Solve using substitution. 2x - 3y = 10 x + y = 0

Answer.) x + y = 0 --> x = -y = 2x - 3y = 10 = 2(-y) - 3y = 10 = -5y = 10 --> y = -2 2x - 3y = 10 = 2x - 3(-2) = 10 = 2x + 6 = 10 --> 2x = 10 - 6 = 2x = 4 --> x = 2

Solve using substitution. y = 3x + 2 x + y = 14

Answer.) x + y = 14 = x + (3x + 2 ) = 14 = 4x = 14 - 2 = 4x = 12 --> x = 3 y = 3x + 2 = y = 3(3) + 2 = y = 9 + 2 --> y = 11

Solve using substitution. x - 2y = 4 x - 3y = 6

Answer.) x - 2y = 4 --> x = 2y +4 = x - 3y = 6 = (2y + 4) - 3y = 6 --> -y = 6 - 4 = -y = 2 --> y = -2 x - 3y = 6 = x - 3(-2) = 6 --> x + 6 = 6 = x = 6 - 6 --> x = 0

Solve using substitution. 4x + 5y = 26 3x = y - 9

Answer.) 3x = y - 9 --> y = 3x + 9 = 4x + 5y = 26 --> 4x + 5(3x + 9) = 26 = 4x + 15x + 45 = 26 = 19x = 26 - 45 --> x = -1 3x = y - 9 --> 3(-1) = y - 9 = -3 = y - 9 --> y = 6

Solve using substitution. y = 3x - 1 x + y = 11

Answer.) x + y = 11 = x + (3x - 1) = 11 --> 4x - 1 = 11 = 4x = 12 --> x = 3 y = 3x - 1 = y = 3(3) - 1 = y = 9 - 1 --> y = 8

Solve using substitution. 2x = 6y + 9 y - 2x = -4

Answer.) y - 2x = -4 --> y = 2x - 4 = 2x = 6y + 9 = 2x = 6(2x - 4) + 9 = 2x = 12x - 24 + 9 --> 2x - 12x = -24 +9 = -10x = -15 --> x = 1.5 y - 2x = -4 = y - 2(1.5) = -4 --> y - 3 = -4 = y = -4 + 3 --> y = -1