Question

How many solutions does the system y = −7x + 3 and y + 7x = 10 have?​

Answer 1

The system of equations y = -7x + 3 and y + 7x = 10 has no solutions because they represent parallel lines with the same slope but different y-intercepts.

Step-by-step explanation:

To determine how many solutions the system of equations has, we can analyze the equations y = -7x + 3 and y + 7x = 10. First, we'll rearrange the second equation into slope-intercept form to see if they describe the same line, a unique line, or parallel lines.

Rearrange y + 7x = 10:

• Subtract 7x from both sides: y = -7x + 10.

Now we have two equations:

• y = -7x + 3
• y = -7x + 10

Both equations have the same slope (-7) but different y-intercepts (3 and 10, respectively). This means that the lines are parallel and do not intersect. Thus, the system of equations has no solutions.

Answer 2

No solutions.

Step-by-step explanation:

y = −7x + 3

y + 7x = 10

Rearranging the first equation we get:

y + 7x = 3

Note that in the last 2 equations we have y + 7x on the left side and a 3 and 10 on the right; y + 7x cannot be equal to 3 and 10, therefore there are no solutions.