How many solutions does the following system of equations have?y=3x−56x−2y=10(1 point)ResponsesInfinitely many solutionsInfinitely many solutions2 solutions2 solutionsNo solutionNo solution1 solution

Answer 1

To determine how many solutions the given system of equations has, we need to analyze the equations. We have:

1. \( y = 3x - 5 \)
2. \( 6x - 2y = 10 \)

Let's first rewrite the second equation to express it in the slope-intercept form like the first equation.

Starting with the second equation: \[ 6x - 2y = 10 \]

We can rearrange this to solve for \( y \):

1. Subtract \( 6x \) from both sides: \[ -2y = -6x + 10 \]

2. Divide each term by -2: \[ y = 3x - 5 \]

Now we see that both equations are actually:

1. \( y = 3x - 5 \)
2. \( y = 3x - 5 \)

Since both equations represent the same line, they have infinitely many solutions. Therefore, the answer is:

Infinitely many solutions.