y = 5x + 7: One Solution
3y - 15x = 18: One Solution
y = 3x + 6: One Solution
y = -13x - 4: One Solution
x - 2y = 6: One Solution
3x - 6y = 18: One Solution
y = 23x - 1: One Solution
y = 23x - 2: One Solution
Therefore, all of the given systems of equations have one solution.
Match the system of equations to the number of solutions it has.%0D%0A%0D%0AYou can use your Graphing Calculator!%0D%0A%0D%0A(4 points)%0D%0APut responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.%0D%0Ay = 5x + 7%0D%0A%0D%0A3y - 15x = 18%0D%0A%0D%0Ay = 3x + 6%0D%0A%0D%0Ay = -13x - 4%0D%0A%0D%0Ax - 2y = 6%0D%0A%0D%0A3x - 6y = 18%0D%0A%0D%0Ay = 23x - 1%0D%0A%0D%0Ay = 23x - 2%0D%0A%0D%0AOne SolutionNo SolutionInfinite Solutions
3 answers
no
Apologies for the incorrect response. Let's re-evaluate the systems of equations.
1. y = 5x + 7
This equation represents a straight line with a slope of 5 and a y-intercept of 7.
2. 3y - 15x = 18
By simplifying the equation, we get y - 5x = 6. This equation represents a straight line with a slope of 5 and a y-intercept of 6.
3. y = 3x + 6
This equation represents a straight line with a slope of 3 and a y-intercept of 6.
4. y = -13x - 4
This equation represents a straight line with a slope of -13 and a y-intercept of -4.
5. x - 2y = 6
By rearranging the equation, we get y = 0.5x - 3. This equation represents a straight line with a slope of 0.5 and a y-intercept of -3.
6. 3x - 6y = 18
By simplifying the equation, we get x - 2y = 6. This equation represents a straight line with a slope of 0.5 and a y-intercept of -3.
7. y = 23x - 1
This equation represents a straight line with a slope of 23 and a y-intercept of -1.
8. y = 23x - 2
This equation represents a straight line with a slope of 23 and a y-intercept of -2.
Now, let's match each system of equations to its respective number of solutions:
1. y = 5x + 7 -> One Solution
2. 3y - 15x = 18 -> One Solution
3. y = 3x + 6 -> One Solution
4. y = -13x - 4 -> One Solution
5. x - 2y = 6 -> One Solution
6. 3x - 6y = 18 -> One Solution
7. y = 23x - 1 -> One Solution
8. y = 23x - 2 -> One Solution
Matching the system of equations to the number of solutions, we have:
One Solution: 1, 2, 3, 4, 5, 6, 7, 8
Therefore, all of the given systems of equations have one solution.
1. y = 5x + 7
This equation represents a straight line with a slope of 5 and a y-intercept of 7.
2. 3y - 15x = 18
By simplifying the equation, we get y - 5x = 6. This equation represents a straight line with a slope of 5 and a y-intercept of 6.
3. y = 3x + 6
This equation represents a straight line with a slope of 3 and a y-intercept of 6.
4. y = -13x - 4
This equation represents a straight line with a slope of -13 and a y-intercept of -4.
5. x - 2y = 6
By rearranging the equation, we get y = 0.5x - 3. This equation represents a straight line with a slope of 0.5 and a y-intercept of -3.
6. 3x - 6y = 18
By simplifying the equation, we get x - 2y = 6. This equation represents a straight line with a slope of 0.5 and a y-intercept of -3.
7. y = 23x - 1
This equation represents a straight line with a slope of 23 and a y-intercept of -1.
8. y = 23x - 2
This equation represents a straight line with a slope of 23 and a y-intercept of -2.
Now, let's match each system of equations to its respective number of solutions:
1. y = 5x + 7 -> One Solution
2. 3y - 15x = 18 -> One Solution
3. y = 3x + 6 -> One Solution
4. y = -13x - 4 -> One Solution
5. x - 2y = 6 -> One Solution
6. 3x - 6y = 18 -> One Solution
7. y = 23x - 1 -> One Solution
8. y = 23x - 2 -> One Solution
Matching the system of equations to the number of solutions, we have:
One Solution: 1, 2, 3, 4, 5, 6, 7, 8
Therefore, all of the given systems of equations have one solution.