Systems of Equations 209
2 x + 2 = 4
2 x = 2
2
2
2
2
x
=
x= 1
Step 5. Check whether x = 1 and y = −2 satisfy both original equations.
24
23
xy
xy+ 222
2224
2 1 43
() 1 ()=+ 2 2
() 1 2 () 1 −
Check. √
Step 6. Write the solution.
The solution is x = 1 and y = −2. That is, the two lines intersect at
the point (1, −2).
Problem Solve the system.
523
23 1
xy 2
xy 3
22 y=
33 y=−
Solution
Step 1. To eliminate y, multiply the fi rst equation by 3 and the second equa-
tion by − 2.
523
23 1
xy 2
xy 3
22 y=
33 y=−
Multiplyby
Multiplyby
3
2
⎯→⎯⎯Multiplyby^3 →→
⎯→⎯→⎯→M lti lb− 2
15 69
462
xy 6
xy 6
+ 66
− 4 =
Step 2. Add the resulting two equations.
15 69
462
11 11
xy 6
xy 6
x
+ 66
− 4 =
=
Step 3. Solve 11x= 11 for x.
11 x= 11
11
11
11
11
x
=
x = 1