the system of equations y=2x - 3 and y=4 x -3 has: here are the mutiple choices :exactly one solution, no solution, infinitely many solutions , exactly two solutions which one is it and choose the description of the system of equations x plus 2y=7 and 3x - 2y=5 the mutiple choices are consistent and independent or consistent and dependent or inconsistent, inconsistent and dependent

Question

the system of equations y=2x - 3 and y=4 x -3 has: here are the mutiple choices :exactly one solution, no solution, infinitely many solutions , exactly two solutions which one is it and choose the description of the system of equations x plus 2y=7 and 3x - 2y=5 the mutiple choices are consistent and independent or consistent and dependent or inconsistent, inconsistent and dependent

Answer 1

What do you think and why? The purpose of these multiple choice algebra equations is to get you to think.

The first pair of equations, if graphed, would result in two intersecting straight lines. That should give you a clue as to the answer.

In the second question. "inconsistent" means that if one equation is true, the other cannot be true. "dependent" means you can derive one from the other. Independent means that you cannot. You decide which terms apply.

Answer 2

i got your clue on the first one but the second i still don't understand could you help me out please

Answer 3

To determine the solution(s) for each system of equations, let's analyze them one by one:

1) The system of equations y = 2x - 3 and y = 4x - 3:
To determine the number of solutions, we need to compare the slopes of the two equations. The slopes are 2 and 4, respectively. Since the slopes are different, they will intersect at a single point, representing exactly one solution. Therefore, the answer is "exactly one solution."

2) The system of equations x + 2y = 7 and 3x - 2y = 5:
To identify the nature of the solution(s), we can use the method of elimination or substitution. In this case, let's use the elimination method:

Multiply the first equation by 2 to match the coefficients of y:
2(x + 2y) = 2(7)
2x + 4y = 14

Now, add the two equations together to eliminate y:
(2x + 4y) + (3x - 2y) = 14 + 5
5x + 2y = 19

The resulting equation, 5x + 2y = 19, cannot be reduced any further. However, it is independent of the original equations and still contains both variables x and y. This means that the system is consistent and independent, having exactly one solution. Therefore, the correct answer is "consistent and independent."