Easy Algebra Step-by-Step

208 Easy Algebra Step-by-Step

Step 4. Check whether x= 3 and y= 2 satisfy both equations.

24

5

xy

xy+=y

2624

325

()()^6 −

() 3 () 2 =+= 32

Check. √

Step 5. Write the solution.

The solution is x= 3 and y= 2. That is, the two lines intersect at the

point (3, 2).

Solving a System of Equations by Elimination

To solve a system of equations by elimination, you multiply the equations by

constants to produce opposite coeffi cients of one variable so that it can be

eliminated by adding the two equations.

Problem Solve the system.

24

23

xy

xy+ 222

Solution

Step 1. To eliminate x, multiply the second equation by −2.

24

23

xy

xy+ 22

⎯→⎯→⎯→

⎯→⎯→⎯→Multiplyby− 2

24

246

xy

− 2 xy 4 =

Step 2. Add the resulting two equations.

24

246

510

xy

xy 4

y

− 2 =

− 5

Step 3. Solve −5y= 10 for y.

−5y= 10

−

−

=

−

5

5

10

5

y

y= −2

Step 4. Substitute −2 for y in one of the original equations, 2x − y = 4, and

solve for x.

2 x − (− 2 ) = 4