Question

HELP. Turn the equation into y=mx+b if not already. Figure out whether it has one solution, no solution or infinite solutions. Use graphing, substitution or elimination.

-3x+3y=4
-x+y=3

(same slope or different slop?)
(same y-intercept or different y-intercept?)
​

Answer 1

Equation 1: y = x + 4/3
Equation 2: y = x +3

No solution, same slope, different y-intercepts.

Explanation:

The two equations have been converted to y=mx+b or slope-intercept form. The slope is the same (1), but the intercepts are different. Equation 1 crosses the y-axis at (0, 4/3), Equation 2 crosses the y-axis at (0,3). Both equations represent parallel lines, so there is no solution because they will never intersect each other.

Answer 2

Starting with the given system of equations:

-3x + 3y = 4

-x + y = 3

To solve for y in terms of x, we can rearrange each equation to the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

For the first equation, we can add 3x to both sides and divide by 3 to obtain:

3y = 3x + 4

y = x + 4/3

So the slope of the first equation is 1 and the y-intercept is 4/3.

For the second equation, we can add x to both sides to obtain:

y = x + 3

So the slope of the second equation is also 1, but the y-intercept is different at 3.

To determine the number of solutions, we can use either substitution or elimination.

Using substitution, we can solve for x in the second equation:

x = y - 3

Then substitute this expression for x in the first equation:

-3(y - 3) + 3y = 4

Simplifying, we get:

-3y + 9 + 3y = 4

9 = 4

This is a contradiction, so the system has no solution.

Alternatively, we can use elimination to solve for y:

-3x + 3y = 4

-x + y = 3

Multiplying the second equation by 3, we get:

-3x + 3y = 4

-3x + 3y = 9

Subtracting the second equation from the first, we get:

0x + 0y = -5

This is a contradiction, so the system has no solution.

In summary, the given system of equations has no solution. The two equations have the same slope but different y-intercepts.

Hope this helps you! I'm sorry if it's wrong. If you need more help, ask me! :]