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