SYSTEMS OF EQUATIONS Substitution Method Ex 1 2

SYSTEMS OF EQUATIONS

Substitution Method Ex. 1: 2 x + y = 15 y = 3 x You have to go back to Wenow have been using the 2 x + 3 x = 3(3) 15 = 9 y = one of your original in equations Substitution Property our proofs. where you will substitute the so 5 x = 15 Nowanswer we are going toordered Write your as an known value of x in use substitution to solve pair order toand determine x = (3, 3 the 9)value of y systems of equations.

Ex. 2 3 x – y = 13 y=x+5 3 x – ( x + 5 ) = 13 3 x – 5 = 13 Now substitute back into one of 2 x = 18 to find y. the original equations y = 9 + 5 = x 14 =9

You may have to rearrange one of the equations before you do the substitution. x + 4 y = 20 Rearrange: x = 20 – 4 y 2 x + 3 y = 10 Now substitute and solve for y: Find x: x + 4(6) = 20 2 (20 – 4 y)+3 y=10 so=4020– 8 y + 3 y=10 x+ 24 -5 y = -30 so y =x 6= -4

Solving systems of equations by adding or subtracting equations Example: x + 5 y = -7 3 x – 5 y = 15 Now substitute into either equation youy: add these to. Iffind 4 x = 8 two equations 2 + 5 y =the -7 5 y = -9 drops out! together, y term x= 2 y = -9/5

Example: 4 x – y = 16 3 x – y = 11 x=5 4(5) – y = 16 20 – y = 16 y=4 (5, 4)

You may have to multiply one of the equations before you add or subtract: -3 x + 2 y = 10 Now add the equations together 4 x -4 2 x–– 2 y y == -2 Multiply this equation by 2 x=6 After substitution we find y = 14 (6, 14)

You may have to multiply both of the equations by a number to get a variable to cancel out. Multiply by 3 6 x 2 x++15 y 5 y == 108 36 3 x-– 4 y 2 y= = 6 x -6 -3 19 y = 114 y= 6 Multiply by 2