We check the solution by substituting 2 for xand 4 for yin bothequations.
CHECK (1) (2)
Substitute. Substitute.Multiply. ✓ True
✓ True
Since 1 2, 4 2 satisfies both equations, the solution set is 51 2, 4 26. NOW TRY
26 = 26
6 + 20 26 4 = 4
3122 + 5142 26 4 2122
3 x+ 5 y= 26 y= 2 x
12 , 42
258 CHAPTER 4 Systems of Linear Equations and Inequalities
Using the Substitution MethodSolve the system by the substitution method.
(1)
(2)Equation (2) gives xin terms of y. Substitute for xin equation (1).
(1)
Let.
Distributive property
Combine like terms.
Add 2.
Divide by 3.To find x, substitute 3 for yin equation (2), , to get
Check that the solution set of the given system is 51 - 4 , 326. NOW TRY
x=- 1 - 3 = - 4.
x=- 1 - y
y= 3
3 y= 9
- 2 + 3 y= 7
- 2 - 2 y+ 5 y= 7
21 - 1 - y 2 + 5 y= 7 x=- 1 - y
2 x+ 5 y= 7
- 1 - y
x=- 1 - y
2 x+ 5 y= 7
EXAMPLE 2
CAUTION A system is not completely solved until values for both x and y are
found.Write the solution set as a set containing an ordered pair.
NOW TRY
EXERCISE 2
Solve the system by the
substitution method.
x=y- 34 x+ 9 y= 1Distribute 2 to
both- 1 and .-yWrite the
x-coordinate first.CAUTION Even though we found yfirst in Example 2,the x-coordinate is
always written first in the ordered-pair solution of a system.
Solving a Linear System by Substitution
Step 1 Solve one equation for either variable.If one of the variables has
coefficient 1 or , choose it, since it usually makes the substitu-
tion method easier.
Step 2 Substitutefor that variable in the other equation. The result should
be an equation with just one variable.
Step 3 Solvethe equation from Step 2.
Step 4 Substitutethe result from Step 3 into the equation from Step 1 to
find the value of the other variable.
Step 5 Checkthe solution in both of the original equations. Then write the
solution set.- 1
NOW TRY
EXERCISE 1
Solve the system by the
substitution method.
y=- 3 x2 x- 4 y= 28NOW TRY ANSWERS
- 51 2, - 626 2. 51 - 2, 1 26
http://www.ebook777.com
http://www.ebook777.com