1. Is there ONE solution, NO solution or INFINITE solution to this system of equations?
y=-2x + 8 and y = 4x - 10
2. Describe the graph with NO solutions to the system of equations?
3. Solve the system of equations by SUBSTITUTION…show work
y= 4x - 6
6x + 2y = 2
4. Solve the system of equations by ELIMINATION…show work
-4x + 6y = 34
2x - 6y = - 32
5. The Math Club sold slices of pizza, p, at a profit of $4 each and cans of soda, "s", at $1 each, to raise money for a trip. They sold 300 items and made a profit of $600. Write the pair of linear equations that model this situation.
1. There is ONE solution to the system of equations.
2. The graph with NO solutions would be two parallel lines that never intersect.
3.
y = 4x - 6
6x + 2(4x - 6) = 2
6x + 8x - 12 = 2
14x - 12 = 2
14x = 14
x = 1
y = 4(1) - 6
y = 4 - 6
y = -2
Therefore, the solution is x = 1, y = -2.
4.
-4x + 6y = 34
2x - 6y = -32
Adding the two equations together:
-2x = 2
x = -1
Substitute x = -1 back into one of the equations:
-4(-1) + 6y = 34
4 + 6y = 34
6y = 30
y = 5
Therefore, the solution is x = -1, y = 5.
5. Let p be the number of slices of pizza and s be the number of cans of soda sold.
The pair of linear equations that model this situation are:
p + s = 300 (total items sold)
4p + s = 600 (total profit made)
These equations represent the total number of items sold and the total profit made.