Question

Match each system on the left with the number of solutions that it has on the right. Answer options on the right may be used more than once.

x = y - 3
2x - 2y = - 6
5x + 2y = -7
10x + 4y = - 14
3y - 6x = 3
4x - 3y = -2
3y - 6x = -3
4x - 2y = -2
a) no solution
b) one solution
c) infinite number of solutions

Answer 1

The systems of equations presented in the question all have one solution.

Step-by-step explanation:

To determine the number of solutions for each system of equations, we need to solve the systems and analyze the results. Here are the solutions for each system:

• x = y - 3: This equation represents a line with a slope of 1 and a y-intercept of -3. It has one solution.
• 2x - 2y = -6: This equation represents a line with a slope of 1 and a y-intercept of -3. It has one solution.
• 5x + 2y = -7: This equation represents a line with a slope of -5/2 and a y-intercept of -7/2. It has one solution.
• 10x + 4y = -14: This equation represents a line with a slope of -5/2 and a y-intercept of -7/2. It has one solution.
• 3y - 6x = 3: This equation represents a line with a slope of 2 and a y-intercept of 1. It has one solution.
• 4x - 3y = -2: This equation represents a line with a slope of 4/3 and a y-intercept of 2/3. It has one solution.
• 3y - 6x = -3: This equation represents a line with a slope of 2 and a y-intercept of -1. It has one solution.
• 4x - 2y = -2: This equation represents a line with a slope of 2 and a y-intercept of 1. It has one solution.

Therefore, all the systems have one solution.