4-1
Write an equation in slope-intercept form that would have infinitely many solutions in a system of equations with 5x - 2y = 8.
(Hint: Change it from explicit form into slope-intercept form by subtracting the X. Make sure that y is always positive and that you divide the numbers to make sure y is 1y and not any other number.
The equation is... y = 5/2x -4
Solve the system of equations by the substitution method.
Don't forget to make it into an ordered pair! (x,y)
x + 8y = 21
2x + 3y = 3
The solution is (-3,3)
4x - 5y = 9
x - 5y = -9
The solution is (6,3)
What type of line is less than and more than?
What type of line is less than or equal to and more than or equal to?
It is a dashed line.
It is a straight line.
Change this equation into standard form.
2x + 3y = 6
y = -2/3x + 2.
If two lines are parallel, what do they make them?
Hint: One of the following answers is correct: infinitely many solutions, one solution, or no solution.
No solution
Solve the equation by using the substitution method! Don't forget to make sure your answer is an ordered pair (x,y).
y = 3x + 1
3y - 4x = 13
The solution is (2,7)
Solve the system of equations using the elimination method.
4x + y = 0
-8x - y = -4
The solution is (1,-4)
If it is greater than you will go two ways depending on the graph. What are the two ways?
If it is less than, you will go two ways depending on the graph. What are the two ways?
You would go up or to the right.
You would go down or to the left.
Change this equation into slope-intercept form.
5x - 2y = 10
y = 5/2x -5
Answer the following question below:
-6x + y = 9
x + 4y = 24
How many solutions does this have?
There is one solution.
Solve the system of equations by the substitution method. Make it an ordered pair.
Hint: This one has the x-axis as a fraction, but the y-axis is still a whole number.
y = x + 9
y = 5x + 10
The solution is (-1/3,25/3)
Hint: The y-axis is a fraction, but the x-axis is a whole number.
3x - 5y = 7
6x + 10y - 10
The solution is (2,-1/5)
What would the y-intercept or y be in this equation?
x < 20
This is because if y is not mentioned, it is not there, and if it is not there, then it would equal 0.
Change this equation into standard form.
-x + 4y = 8
y = 1/4x + 2
If two lines are not parallel, then this system of equations will have. . .
A) A solution
B) No solution
C) infinitely many solutions
A or C is correct because they can be intersecting if not parallel, and they could also be the same, which would be infinitely many solutions.
Solve the system of equations by substitution. Make it an ordered pair.
y=4x - 13
2x + 37 = 17
The solution is (4,3)
Ann Marie Jones has been pricing train fares for a group trip to New York. Three adults and four children must pay $115. Two adults and three children must pay $82. Find the price of the adult's ticket and the price of a child's ticket.
The price of a child's ticket is $__.
The price of an adult's ticket is $__.
The price of a child's ticket is $16.
The price of an adult's ticket is $17.
-5y > -5.
What would x equal in this equation?
Would this line be horizontal or vertical?
This line would be vertical because y is up and down, and x is left and right.
Sarah and Tom mowed the lawns together and earned $180. Because Tom provided the gas and maintenance for the mower, he is entitled to $20 more than Sarah. How much money does each person receive?
Sarah gets $80.
Tom receives $100.
Would the slope go up or down if the number is negative?
Down
Use the substitution to solve the system of equations.
Hint: This one might have infinitely many solutions or no solution.
2x + 4y= -12
y = -1/2x + 7
There is no solution
Find the value of b so that the system has an infinite number of solutions.
3 x + 3 y = b
y= 53x + 3y = b
b = ?
b = 15
Which way would the line be if it x=0 and y=0?
If y=0, then the line would be horizontal because x is left and right.
If x=0, then the graph would be vertical because y is up and down.
Sarah and Mike earned a total of $1400 from a joint project. They agreed that Sarah, who managed the project logistics, should receive $200 more than Mike, who handled the technical work.
Write a system of linear equations to represent this situation.
y = mx OR in this case S = M + B
S = M + 200