Subsitution
What is the first step (the thing you need to do) in substitution?
solve for one variable
What is the first step in solving this system using elimination?
−6x − 9y = 0
−24x = 36y
Line up your variables
Graph 1
What is the solution?
(-2,-1)
Is the ordered pair (0, −5)
a solution to the system?
y = 4x − 9
y = x − 3
no
Solve for x -- Get x by itself:
2x + 6y = 8
x=-3y+4
If you have already found
x = 3, find y:
-2x + 6y = 6
-7x +8y = -5
y=2
What coefficients would you multiple your x terms in each equation to solve the system?
3x + 5y = -10
5x - 2y = 8
3x * 5 or -5
5x * 3 or -3
One positive, one negative
Graph 2
What is the solution?
No Solution
Is the ordered pair (3, −5)
a solution to the system?
6x + 8y = −22
y = −5
yes
What type of lines have
“no solution”
Parallel lines
Substitute
y = 3x + 2
into
x - 2y = 11
and solve for x
x=-3
Eliminate y and
solve for x.
-2x - 9y = -25
-4x - 9y = -23
x=-1
Graph the system and find the solution:
y = − 1/4 x − 4
y = 5/4 x + 2
(−4, −3)
What is the solution to the system?
-5x + 10y = 2
y = 1/2x - 1/5
infinitely many solutions
Write two equations to go with the situation:
Zach has nickels and dimes worth $1.40. There are 17 total coins. Use 'n' for nickels and 'd' for dimes
n+d=17
0.05n+0.10d=1.40
Solve the system:
x + 8y = −15
7x + 8y = −9
(1, −2)
Eliminate x and solve for y.
4x + 8y = 20
-4x + 2y = -30
y=-1
Graph the system and find the solution:
y = - 3x + 4
y + 3x = - 4
Infinitely Many Solutions
Is the ordered pair (6, −6)
a solution to the system?
−24 − 8x = 12y
1 + 5/9 y = − 7/18 x
yes
Solve the system:
−9x − 3y = −2
y = −3x − 4
no solution
Solve the system:
−5x − 7y = 11
x − 2y = −9
(−5, 2)
Solve the system:
−9 + 5y = −4x
−11x = −20 + 9y
(1, 1)
Graph the system and find the solution:
7x − y = 3
x − y = −3
(1, 4)
Write a system of equations with the solution (4, −3).
check
Write two equations to go with the situation:
Anna bought 3 hats and 2 scarfs for $34. Sara bought 1 hat and 4 scarfs for $28.
How much does a hat cost?
$8