Question

Rhoda is asked to graph this system of equations: 5x - 6y = 4 3y + 2x = 7 How many times will the lines intersect? O A. The lines will intersect infinitely many times, because they are identical. O B. The lines will not intersect, because this system has no solutions. O C. The lines will intersect once, because this system has one solution. D. There is no way to tell without graphing the lines first.​

Answer 1

C. The lines will intersect once, because this system has one solution

Explanation:

Answer 2

• C. The lines will intersect once, because this system has one solution

Explanation:

System of equations:

• 5x - 6y = 4
• 3y + 2x = 7

The system of linear equations has one solution if the lines intersect, no solution if the lines are parallel, infinitely many solutions if lines are same

Let's put the lines into slope-intercept form to compare

Line1

• 5x - 6y = 4
• 6y = 5x - 4
• y = 5/6x - 4/6

Line 2

• 3y + 2x = 7
• 3y = -2x + 7
• y = -2/3x + 7/3

As we see lines have different slopes so they are different and they intersect once

This system has one solution