University:
High School
Course:
High School Algebra
Academic year:

2020
Views:

290

Pages:

6
Author:

Prexl20

Solving 3 Systems of Equations In your own words, write the meaning of each vocabulary term. linear equation in three variables looks like 2x + 5y - 3z = 11 system of three linear equations means we will have 3 equations solution of a system of three linear equations is the answer to the 3 linear system in a (x, y, z) format ordered triple has x = y = z = When Solving a Three-Variable System Step 1 Rewrite the linear system in three variables as a linear system in two variables by using the substitution or *elimination method. easier to use ... but you pick. Step 2 Solve the new linear system for both of its variables. Step 3 Substitute the values found in Step 2 into one of the original equations and solve for the remaining variable. When you obtain a false equation, such as 0 = 1, in any of the steps, the system has no solution. When you do not obtain a false equation, but obtain an identity such as 0 = 0, the system has infinitely many solutions. See the Following examples and use half to a full page to solve each problem! The trick to solving 3 equations with 3 variables is to... ...Eliminate one variable and one equation ...your pick Combine two equations... ...to end up with 2 equations with 2 variables (make sure to get that third one in there) Add x + y + z = 1 x - y - z = 3 2x = 4 2x / 2 = 4 / 2 x = 2 That worked out really nicely Now solve for the last variable (pick one of the original equations) x + y + z = 1 (2) + y + (0) = 1 2 + y = 1 y = -1 Double Check your answers - and guarantee they work! (2) + (-1) + (0) = 1 ✓ -(2) - (-1) + (0) = -1 ✓ It isn't always this easy! It doesn't matter which other equation you pick... as long as it isn't the one you already used.