Solving by Graphing
What is the solution to a system where the lines intersect?
The point of intersection (x,y)
Solve for x if y = 5x - 10 and 2x - 5y = -19.
x = 3
If two lines in a system have the same slope but different y-intercepts, how many solutions are there?
No solution (the lines are parallel)
The sum of two numbers, x and y is 30. Their difference is 10. What are the two numbers?
10 and 20
When graphing an inequality with a > or a < symbol, should the line be solid or dashed?
Dashed
Solve this system by graphing: y = -4 and
y = -5/3x + 1.
(3, -4)
Solve using elimination: 5x + 10y = 25 and -5x - 9y = -20.
(-5, 5)
What value of d makes this system have infinitely many solutions? 3x - 2y = 9 and -6x + 4y = 2d.
d = -9
The sum of two numbers, m and n, is 40. Their difference is 20. What is the quotient of the two numbers?
3
If you are graphing y > 2x + 3, do you shade above or below the line?
Identify the point of intersection for y = -x - 2 and
y = x - 4.
(1, -3)
Find the value of x for the system: 8x - 5y = -17 and 10x + y = 15.
x = 1
What value of k results in no solution? 2x + 5y = 7 and 2xk + 10y = 21.
k = 2
If a + b = 30 and a - b = 10, what is the value of a/b?
2
Is the point (0,0) a solution to the system y < x + 5 and y > x - 2?
Yes
Solve this system by graphing:
y = -1/2x + 2
y = 3/2x - 2
(2, 1)
Solve the system using any method:
3x - 2y = 2
5x - 5y = -10
(6, 8)
How many solutions does the following system have?
2x + y = 4
6x + 3y = 12
Infinitely many solution
A farm has only chickens (c) and cows (w). There are 30 heads and 100 legs total. How many cows are on the farm?
20 cows
Write the system of inequalities for this scenario: You want to buy at least 10 items. Notebooks (n) cost $2 each and Pens (p) cost $1 each. You have a maximum of $15 to spend.
n + p ≥ 10
2n + 1p ≤ 15
Given the system y = 3x - 5 and x + y = 3, what is the point of intersection?
(2,1)
If x + y = 10 and x - y = 4, what is the value of
x2 - y2?
40
For what value of a will the following system have no solution?
y = 5x + 2
ax - 2y = 10
a = 10
If 2x + y = 10 and 3x - y = 5, what is the value of
x + y?
7
Is the point (2, 5) a solution to the following system?
y > 3x - 2 and y ≤ -x + 8
Yes