Solving Systems
Using Substitution
Common Core State Standards
A-REI.C.6 Solve systems of linear equations exactly and
approximat ely (e.g., w it h graphs), f ocusing on pairs of
linear equations in two variables.
MP 1, MP 2, MP 3, M P4Objective To solve system s of eq u atio n s using substitutionGet t i n g Re a d y! OX C
How can you get
st ar t ed? One
house equals 3 cars
plus $100. Two
houses equal...A board game allows players to tra d e game
pieces o f equal value. The diagram shows
tw o f a i r t r a d e s. T h e h o te l is w o r t h $ 2 4 0 0.
H o w m uch is a c a r w o r t h? E x p la in y o u r
reasoning.I*
IzlMATHEMAiicAt You can m odel fair trades w ith a linear system. You can solve linear system s by solving
PRACTICESLesson
Vocabulary- substitution
method
one of th e equations for one of the variables. Then substitute the expression for the
variable into th e o th er equation. This is called th e substitution method.Esse n t i a l U n d e r st a n d i n g Systems of eq u atio n s can b e solved in m ore th a n one
way. W hen a system h as at least one eq u a tio n th a t can be solved quickly for a variable,
th e system can be solved efficiently using substitution.How can you get
started?
If one e q u a tio n is already
solved for one variable,
use it fo r th e sub stitu tio n.
If both equations are
solved fo r a variable, you
can use either one.Using Substitution
W h at is th e so lu tio n of th e system? U se su b stitu tio n.Step 1y = 3x
x + y = — 32
Because y = 3x, you can substitute 3x fory in x + y = —32.
x + y = -32 Write the second equation.
x + 3x — -32 Substitute 3x for y.
4x = —3 2 Si mp l i f y.
x — -8 Divide each side by 4.
S te p 2 Substitute - 8 for x in eith er eq u a tio n a n d solve fory.
y = 3x Wri t e ei t her equat i on,
y = 3(-8) = -24 Substitute -8 for x and solve.
The solution is ( - 8 , -2 4 ). Check by substituting ( - 8 , -2 4 ) into each equation.372 Chapter 6 Systems of Linear Equations and Inequalities