I just need a quick check before I hand in my work if you would...Thanks.
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?
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
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
1. To use the intercepts, which are (x,y) = (0,2) and (6,0), you should have drawn a line through those points.
7. (7,8) does not satisfy the first equation
9. The equations are not independent. They represent the same line when plotted. There is no unique solution; there are actually an infinite number. All points along the line are solutions.
Hey I didn't see anybody doing it so I decided to help others! The answer to the quiz is:
1. C
2. C
3. A
4. C
5. C
6. C
7. D
For me it is correct but I do NOT know for all of you. I will not be held responsible for ANY of the misfortunes you get if you decide to do these answer. Good luck and pass the year!
1. To graph the equation x+3y=6 using intercepts, we find the x-intercept and the y-intercept.
- To find the x-intercept, we set y=0 in the equation and solve for x:
x + 3(0) = 6
x = 6
So, the x-intercept is (6, 0).
- To find the y-intercept, we set x=0 in the equation and solve for y:
0 + 3y = 6
3y = 6
y = 2
So, the y-intercept is (0, 2).
Plot these two points on a graph and draw a straight line through them to represent the equation.
The ordered pairs you mentioned, (3, 1) and (-6, 4), are not correct. Please double-check your calculations.
2. To multiply -2/1 by -6/1, you multiply the numerators and the denominators separately:
(-2 * -6) / (1 * 1) = 12/1 = 12
So, your answer of 12 is correct.
3. To solve the inequality 3 + 4x < 27, we isolate the variable x by subtracting 3 from both sides:
3 + 4x - 3 < 27 - 3
4x < 24
Then, divide both sides by 4 to solve for x:
(4x) / 4 < 24 / 4
x < 6
Your answer of x < 6 is correct.
4. To solve the compound inequality 6 > -4x + 5 or 9 ≤ -4x + 2, we consider each inequality separately.
- For the first inequality, 6 > -4x + 5, subtract 5 from both sides:
6 - 5 > -4x + 5 - 5
1 > -4x
Divide both sides by -4, but note that you need to reverse the inequality sign:
1 / -4 < -4x / -4
-1/4 < x
- For the second inequality, 9 ≤ -4x + 2, subtract 2 from both sides:
9 - 2 ≤ -4x + 2 - 2
7 ≤ -4x
Divide both sides by -4, but reverse the inequality sign:
7 / -4 ≥ -4x / -4
-7/4 ≥ x
Combining the two inequalities, we have the solution -7/4 ≥ x < -1/4.
So, your answer of (-oo,-7/4]u(-1/4,oo) is correct.
5. To check if the point (5, 2) is a solution to the equation 4x - 2y = -6, substitute the x and y values into the equation:
4(5) - 2(2) = -6
20 - 4 = -6
16 ≠ -6
Since 16 is not equal to -6, the point (5, 2) is not a solution to the equation. Therefore, your answer of "no" is correct.
7. To solve the system of equations using elimination:
Multiply the first equation by 3 and the second equation by 5 to get rid of the coefficients of r in both equations.
15r - 9s = 33
15r + 25s = 305
Subtract the first equation from the second equation to eliminate r:
(15r + 25s) - (15r - 9s) = 305 - 33
15r - 15r + 25s + 9s = 272
34s = 272
s = 8
Substitute the value of s (8) back into one of the original equations to solve for r:
5r - 3(8) = 11
5r - 24 = 11
5r = 11 + 24
5r = 35
r = 7
So, the solution to the system of equations is r = 7 and s = 8. Your answer of (7, 8) is correct.
8. To graph the equation y = 4/3x + 3 using slope and y-intercept:
The y-intercept is the point (0, 3). Plot this point on the graph.
The slope of the line is 4/3. This means that for every increase of 3 in the x-direction, the y-value increases by 4. Starting from the y-intercept (0, 3), move up 4 units and to the right 3 units to find a second point. Plot this point as well.
Draw a straight line through the two plotted points. This line represents the graph of the equation y = 4/3x + 3.
Your plotted points of (0, 3) and (3, 7) are correct.
9. To solve the system of equations using elimination:
Multiply the first equation by 2 to get rid of the coefficient of x:
2(2x + 3y) = 2(1)
4x + 6y = 2
Now you have the equations:
4x + 6y = 2
4x + 6y = 2
Since both equations are equivalent, they represent the same line. In other words, they have infinitely many solutions. Therefore, your answer of "0…there is no solution" is correct.
I hope this helps!