Easy Algebra Step-by-Step

Systems of Equations 207

20

3

xy

xy+=y

2220

123

()) () 2 −

()^1 ()^2 =^1 =

Check. √

Step 5. 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.

24

5

xy

xy+=y

Solution

Step 1. Solve the second equation, x+y= 5, for x in terms of y.

x+y= 5

x+y − y= 5 − y

x= 5 − y

Step 2. Substitute 5 − y for x in the fi rst equation, 2x − y = 4, and solve

for y.

2(5 − y) − y= 4

10 − 2y − y= 4

10 − 3y= 4

10 − 313 y 044 − 10

−3y = −6

−

−

=

−

−

3

3

6

3

y

y = 2

Step 3. Substitute 2 for y in the second equation, x+y= 5, and solve for x.

x+ ( 2 ) = 5

x+ 2 = 5

x+ 2 − 2 = 5 − 2

x= 3

When you use the substitution

method, it makes no difference

which equation is solved fi rst or

for which variable, but when you

solve it, be sure to substitute the

value in the other equation.