④-①
What is the solution of the system of equations? y=-2x-4 , y=0.5x+6
(-4,4)
When is it best to use the substitution method?
When one of the equations has a coefficient of 1 or -1.
When is it best to solve a system of equations by the elimination method?
When you end up with like terms that are opposites (negative/positive) in a system of equations.
Is (0,1) a solution to the inequality y>x+1?
Yes, (0,1) is a shaded point on the graph of y>x+1.
Is (1.5, -0.5) a solution to the system of linear inequalities y>x-2 and y≤-x+1?
Yes, the point (1.5, -0.5) is shaded on the region of the system of inequalities.
What is the solution to the system of equations? x-3y=-6 , y=1/3x+2
There are infinitely many solutions.
What is the solution of the system of equations 6x+3y=36 and y=3x+2
(2,8)
Solve the system of equations 3x-7y=16 and 5x-4y=19 by elimination.
(3,-1)
Is (0,2) a solution to the inequality y>x+2?
No, it is not a point on the shaded region.
What would the system of inequalities y>x-2 and y≤-x+1 look like on a graph?
They would intersect with y>x-2 being a dashed line shaded above and y≤x+1 a solid line shaded below.
A friend group with 2 girls and 4 boys spent $32 to get into a party. Another friend group with 6 girls and 3 boys spends $42. What is the price for a girl to get into this party?
x=4 , therefore it costs $4 for a girl to get in.
Gio starts a tapestry brand. In her business, she has expenses and revenue. Her expenses are the cost of her advertising deal ($200) and the discount directly from the promotion ($10 off). Her revenue is $37 per blanket. At what point will Gio exceed her expenses?
Since the system of equations is y=10x+200 and y=37x , Gio will need to sell 8 blankets before her revenue exceeds her expenses.
Ibrahim is making regular desert baskets(3 cupcakes and 2 complimentary gifts) and small desert baskets(4 cupcakes and 3 complimentary gifts). He has 10 cupcakes and 7 complimentary gifts to put in the baskets. How many of each type of basket can he make?
He has enough cupcakes and gifts to make 2 regular baskets and 1 small basket.
Describe how the graph of x≤x-1 would look.
A solid line with all points less than or equal to x-1 shaded below.
What would the graph of y≥-x+2 and y<-x-2 look like?
The graph of y≥-x+2 would be a solid line shaded up. The graph of y<-x-2 would be a dashed line shaded down. The graphs do not overlap.
What is the solution to the system of equations? 2x+y= 4 , y= -2x - 5
There is no solution.
Durtrious says that the solution of the system of equations 5x-y=-4 and y=5x-4 is (1,-1). Kentrell however believes that there is no solution. Use the substitution method to determine who is correct.
There is no solution therefore Kentrell is correct.
In order to solve for a variable using elimination method, what must you do to the other variable?
If it's positive, multiply it by a negative first variable. If it was already negative, just multiply it by the first variable.
Describe how the graph of y<2 would look.
A dashed horizontal line shaded downward.
How can you determine if a graph is less than, less than or equal to, greater than or greater than or equal to?
If the lines are ≤ or < then it's less than and should be shaded below/left. If the lines are ≥ then its greater than and should be shaded above/right. If the signs are ≥ / ≤ then it should be a dashed line. If the lines are > / < then it should be a solid line.
Why is the point of intersection for a system of equations considered it's solution?
when two lines intersect, the co-ordinates of the intersection point satisfy both equations, so it is known as the solution.
What is the solution of the system of equations? 6x-2y=5 and -3x+y=7
There is no solution.
Solve the system of equations by elimination. 3x+4y=10 and 2x+3y=7
(2,1)
Is (2,1) a solution to the inequality y< -1/2x+2?
Yes, (2,1) is a shaded point on the graph of y<-1/2x+2
What is the solution to the system of inequalities y≥-x+2 and y<-x-2 ?
They do not overlap, so there is no solution.