Easy Algebra Step-by-Step

210 Easy Algebra Step-by-Step

Step 4. Substitute 1 for x in one of the original equations, 5x+ 2 y= 3, and

solve for y.

5( 1 ) + 2 y = 3

5 + 2 y = 3

5 + 2 y − 5 = 3 − 5

2 y = −2

2

2

2

2

y

=

−

y= −1

Step 5. Check whether x = 1 and y = −1 satisfy both original equations.

523

23 1

xy 2

xy 3

22 y=

33 y=−

52 523

23 23 1

2

3

() ()^1 =^5 =

() 3 () 1 = 2 =−

Check. √

Step 6. Write the solution.

The solution is x = 1 and y = −1. That is, the two lines intersect at

the point (1, −1).

Solving a System of Equations by Graphing

To solve a system of equations by graphing, you graph the two equations and

locate (as accurately as possible) the intersection point on the graph. Because

graphing devices such as graphing calculators and computer algebra systems

require the slope-intercept form of the equation of

straight lines, the steps will include writing the equa-

tions in that form. (See Chapter 17 for a discussion of

the slope-intercept form.)

Problem Solve the system.

253

321

xy 5

xy 2

55 y=

2 y=

The graphing method might

yield inaccurate results due to

the limitations of graphing.