Easy Algebra Step-by-Step

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