I have a few problems I need you to take a look at and tell me if I arrived at the right answer.

1. I am to use the intercepts to graph the equation x+3y=6
I used the formula y=mx+b using 3 and -6 for x I got these as my ordered pairs to graph (3, 1), (-6, 4)…Is this correct? I also got these two ordered pairs (0, 2) (3, 1)
2. Multiply -2/1*(-6/1): I got 12
3. Solve 3+4x<27 I got <6
4. Solve the compound inequality: 6>-4x+5 or 9 <(or equal to)-4x+2
My answer was (-oo,-7/4]u(-1/4,oo)
5. Is (5,2) a solution to 4x-2y=-6 I said no
6. Decide if the line is parallel, perpendicular or neither
5x+4y=2
4x-5y=4 I said neither
7. Solve using elimination: 5r-3s=11
3r+5s=61 I got (7, 8)
8. Graph using slope and y intercept: y=4/3x+3 I graphed (0, 3) and (3, 7)
9. Solve using elimination
2x+3y=1
4x+6y=2
I got 0…there is no solution

I posted this yesterday twice and then today, I am getting passed over, all I need is a check to see if I am doing my work right. Thank you.

Let's go through each problem and verify the answers:

1. To graph the equation x + 3y = 6 using intercepts, you need to find the x-intercept and the y-intercept. To find the x-intercept, set y = 0 and solve for x: x + 3(0) = 6 => x = 6. So the x-intercept is (6, 0). To find the y-intercept, set x = 0 and solve for y: 0 + 3y = 6 => y = 2. So the y-intercept is (0, 2). The ordered pairs you obtained are not correct. The correct intercepts are (6, 0) and (0, 2).

2. To multiply -2/1 * -6/1, you just multiply the numerators and the denominators: (-2/-6) = (2/6) = 1/3. So the correct answer is 1/3, not 12.

3. To solve the inequality 3 + 4x < 27, you can start by subtracting 3 from both sides: 4x < 24. Then divide both sides by 4: x < 6. So the correct answer is x < 6, not < 6.

4. The compound inequality 6 > -4x + 5 or 9 ≤ -4x + 2 can be solved separately. For the first part, subtract 5 from both sides: -4x + 5 < 6 => -4x < 1. Divide by -4, remembering to flip the inequality sign: x > -1/4. For the second part, subtract 2 from both sides: -4x + 2 ≤ 9 => -4x ≤ 7. Divide by -4, remembering to flip the inequality sign: x ≥ -7/4. Combining the two solutions, the correct answer is x > -1/4 or x ≥ -7/4, not (-oo, -7/4] u (-1/4, oo).

5. To check if (5, 2) is a solution to 4x - 2y = -6, substitute the values of x and y into the equation: 4(5) - 2(2) = 18, not -6. Therefore, you are correct in saying that (5, 2) is not a solution to the equation.

6. To determine if the two lines are parallel, perpendicular, or neither, you need to compare their slopes. In slope-intercept form (y = mx + b), the slope is the coefficient of x. For the first equation, the slope is -5/4, and for the second equation, the slope is 4/5. Since the slopes are not equal or negative reciprocals of each other, the lines are neither parallel nor perpendicular. You are correct.

7. To solve the system of equations using elimination, you can multiply the first equation by 5 and the second equation by -3, then add the two equations together to eliminate the variable s. The resulting equation will give you the value of r: 25r - 15s = 11 and -9r - 15s = -183. Adding the two equations gives 16r = -172, which simplifies to r = -172/16 = -43/4. Substituting this value back into either of the original equations will give you s: 5(-43/4) - 3s = 11 => -215/4 - 3s = 11. Solving for s gives s = 8. So the correct solution is r = -43/4 and s = 8, not (7, 8).

8. To graph the equation y = (4/3)x + 3, you can start by identifying the y-intercept, which is the point (0, 3). Then you can use the slope, which is 4/3, to find another point. To do this, you can use the rise-over-run method: from the y-intercept, you go up 4 units and right 3 units to get the point (3, 7). Plot these two points and draw a straight line through them to graph the equation correctly.

9. To solve the system of equations using elimination, you can multiply the first equation by 2 and the second equation by -1, then add the two equations together to eliminate the variable y. The resulting equation will give you the value of x: 4x + 6y = 2 and -4x - 6y = -2. Adding the two equations gives 0 = 0. This means that the two equations are dependent and represent the same line. Therefore, there are infinitely many solutions to this system, not 0.

I hope this helps clarify your answers! Let me know if you have any further questions.