How can you show
t h a t t h is is a s o lu tio n
to the original
system?
S ubstitute ( - 1 , 2 ) in th e
original system.How can you get
started?
Find th e LCM o f th e
c o e fficie n ts o f the
variable that you want
to eliminate. M ultiply
to make the coefficients
equal to the LCM.
^QS& DSolving a Syst em by Multiplying One Equation
What is the solution of the system? Use elimination. —2x + 15y = —32
7x — 5y = 17Know. -— h- jte eiL. „
A system of equations that The solution of the Multiply one or both equations
c a n 't q u ic kly be solved by system by a c o n s ta n t so th a t th e
graphing or substitution coefficients of one variable are
the same or opposites. Then
eliminate the variable.Step 1 To elim inate one variable, you can m ultiply 7x - 5y = 17 by 3 a n d th e n add.
-2x + 15y = - 3 2 - 2 x + 15y = - 3 2
7x — 5y = 17 Multiply by 3. 2 1 x - 15y = 51
19x + 0 = 19 Add t he equat i ons.
x = 1 Solve for x.
Step 2 Solve for th e elim inated variable. Use eith er of th e original equations.
7x - 5y = 17 You can use the second equation.
7(1) — 5y = 17 Substitute 1 forx.
y = —2 Solve for y.
The solution is (1, - 2 ).
j W
& Got It? 3. a. How can you use th e M ultiplication P roperty of Equality to change —5x - 2y = 6
an eq u a tio n in this system in order to solve it using elim ination? 3x + 6y = 6
b. W rite an d solve a revised system.
c. Show th a t th e solution of th e revised system is a solution of the
original system.Pr o b l em 4 Solving a Syst em by Multiplying Both Equations
What is the solution of the system? Use elimination. 3x + 2y = 1
4x + 3y = - 2
Step 1 M ultiply each eq u a tio n so you can elim inate one variable.
3x + 2y = 1 Multiply by 3. 9x + 6y = 3
4x + 3y = —2 Multiply by 2. 8x + 6y = —4
x + 0 = 7 Subtract the equations.
Step 2 Solve for th e elim inated variable. Use either of th e original equations.
3x + 2y = 1 You can use the first equation.
3(7) + 2y = 1 S u b s titu te 7 fo r x.
2y = - 2 0 S u b tra c t 21 fr o m ea ch side. S im p lify.
y=—10 Solve for y.
The solution is (7, - 1 0 ).3 8 0 Chapter 6 Sy st e m s o f Eq u a t i o n s a n d I n e q u a l i t i e s