Create a graph that shows the point of intersection, P, of line a, graphed below, and line b whose equation is
4y – 5x = 10 ?
10
-10
10
a
-10
What is the value of y for the solution to this system of equations?
{
3
y = 5x + 4
x = -20
The amount, a, earned by Harriet and Demi by depositing money for a period of time, t, is the solution to these
equations:
{
5a = 1800t + 25000
1.2a = 1440t + 16500
What is the solution to this system of equations?
What is the solution to this system of equations?
{
4x + 4y = 8
y=x+5
What is the solution, (x,y), to this system of equations?
{
3y – 5x = 15
x – 2y = 3
Eliza solved this system of equations:
{
What is the solution, (x,y) ?
1
𝑥+
4
1
𝑥+
2
1
𝑦 = 10
8
1
𝑦=2
3
Loui’s towing company charges a base rate of $80 plus $5.50 per mile for each mile over 2. Milo’s towing company
charges a base rate of $60 plus $6.00 per mile for each mile over 2. For what total mileage will both companies charge
the same amount?
What is the solution to this system of equations?
{
y + 2x = 7x + 5
8 – y = 2x + 3y
This is the graph of ⃡𝑃𝑄 .
P
10
8
6
4
2
-10
-8
-6
-4
-2
-2
-4
2
4
6
8
10
Q
-6
-8
-10
What is the point of intersection of ⃡𝑃𝑄 and the line whose equation is -2x + y = 18 ?
Create a graph that shows x – 7 ≤ y < x + 7 ?
Given the inequality 3x - 4y > 12:
A. Graph the inequality in the standard coordinate plane. Show your algebraic work that you used to
graph the inequality and the work you used to determine the direction of the shading for the solution
set of the inequality. Explain how you found your answer.
B. Use the graph to find points in the solution set of the inequality that satisfy each of the given
properties:
i. The x-coordinate and the y-coordinate are both positive.
ii. The x-coordinate is positive, and the y-coordinate is negative.
iii. The x-coordinate is negative, and the y-coordinate is positive.
Verify algebraically that the points you chose are in the solution set of the inequality.
Ashley needs to solve the system of equations by elimination. Her work and solution are shown.
{
Step 1
3x + 2y = 8
4x – 5y = -15
3x + 2y = 17
5x – 5y = -5
Step 2
Step 3
Step 4
Step 5
Step 6
Step 7
×5
→
×2
→
15x + 10y = 85
10x – 10y = -10
5x
= 75
x = 15
15(15) + 10y = 85
165 + 10y = 85
10y = 250
y = 25
(25,15)
A. For each step, explain what Ashley did incorrectly.
B. Check Ashley’s solution. Show your work algebraically, and explain what your result tells you about her
solution.
Given this system of linear equations:
{
x - 4y = 2
5x – 2y = 19
A. Solve the system of equations using the substitution method. Write your answer as an ordered pair.
Show your work algebraically, and explain how you found your answer.
B. Verify that your solution is correct. Show your work algebraically.