Solve by ELIMINATION
2x-4y=2
x+4y=7
(3,1)
y=-x+7
y=x+3
(2,5)
Solve the systems of equations using substitution.
x = 5
x + y = 12
(5, 7)
What kind of lines have no solution?
Parallel lines
Brenda's school is selling tickets to a spring musical. On the first day of ticket sales the school sold 3 senior citizen tickets and 9 child tickets for a total of $75. The school took in $67 on the second day by selling 8 senior citizen tickets and 5 child tickets. What is the price each of one senior citizen ticket and one child ticket?
Senior citizen: $4
Child:$7
-3y-4x=-11
3y-5x=-61
(8,-7)
y=-2x-3
y=-3/2x-4
(2, -7)
Solve the systems of equations using substitution.
y = 2x
x + y = 9
(3, 6)
How can we determine the solution to a system of equations when graphing?
The solution is where the lines of the equations intersect.
Matt and Ming are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Matt sold 3 small boxes of oranges and 14 large boxes of oranges for a total of $203. Ming sold 11 small boxes of oranges and 11 large boxes of oranges for a total of $220. Find the cost each of one small box of oranges and one large box of oranges.
Small box: $7
Large Box: $13
-3y+5x=26
-2y-5x=-16
(4,-2)
y=2x-1
y=-x+2
(1, 1)
Solve the systems of equations using substitution.
x -5y=36
2x+y=-16
(-4,-8)
Without graphing how can you determine the systems is inconsistent?
y=2x-5
y=2x+7
The slope is the same therefore the lines will be parallel and never touch
Find the value of two numbers if their sum is 12 and their difference is 4.
4 and 8
2x-8y=9
2x-3y=9
(4.5,0)
y=-3/2x+2
y=3x+2
(0,2)
Solve the systems of equations using substitution.
x = 3y
x - 3y = 0
Infinitely many solutions
What method would you use to solve this system?
-2y-3x=8
4y-2x=16
elimination
(-4,2)
The difference of two numbers is 3. Their sum is 13. Find the numbers.
5 and 8
2x+4y=3
3x+6y=8
No solution
y=-x+2
y=-x+1
No Solution
Solve the systems of equations using substitution.
2x-3y=-24
x+6y=18
(-6,4)
y=7x+2
y=3x+2
(0,2)
The sum of the digits of a certain two-digit number is 7. Reversing its digits increases the number by 9. What is the number?
34