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Chapter 4: Q 27 (page 386)

Without graphing, determine the number of solutions and then classify the system of equations.

5x+3y=42x-3y=5

Short Answer

Expert verified

The number of solution is one and the system of equations is intersect lines, consistent and independent.

Step by step solution

01

Step 1. Given information

The system of equations is5x+3y=42x-3y=5

02

Step 2. Solve the first equation for y and find the slope and y-intercept. 

5x+3y=43y=-5x+4y=-53x+43

Here the slope is role="math" -53

And they-intercept is43

03

Step 3. Solve the second equation for y and find the slope and y-intercept. 

2x-3y=53y=2x-5y=23x-53

04

Step 4. Required answer

Here the slopes are different.

Therefore, the system of equation is intersect lines with one solution and is consistent and independent.

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