Equal Values
What is one reason that you would choose to solve by equal values?
Both equations are solved for the same variable.
What is one reason that you would choose to solve by substitution?
1 equation is solved for a variable.
-4x-2y=-12
4x+8y=-24
(6,-6)
What method would you use if you had the following system of equations?
y=x+5
4x+y=20
Substitution (because the top equation is solved for y)
How many equations are in a system of equations?
2 or more
y=x+3
y=2x+5
(-2,1)
y = -2
4x - 3y = 18
(3,-2)
-6x + 5y = 1
6x + 4y = -10
(-1, -1)
What method would you use if you had the following system of equations?
-x+y=5
x-5y=-9
Elimination because when you add these, the x's cancel out.
How should your answer be written when solving systems?
As an ordered pair (x,y)
x=2y-4
x=-8y+16
(0,2)
2x - 3y = -1
y = x -1
(4,3)
7x + 2y = 24
8x + 2y = 30
(6, -9)
8x + y = -16
-3x + y = -5
(-1, -8)
How do you check your answer when solving systems of equations?
You plug the ordered pair back into both equations and see if you get the same number on both sides of the equals sign for both equations.
Graph it in Desmos
x=y-8
x=-y
(-4,4)
y = -3x + 5
5x - 4y = -3
(1,2)
5x + y = 9
10x - 7y = -18
(1,4)
-4x + 9y = 9
x - 3y = -6
(9,5)
It is possible to have no solution to a system of linear equations. When graphing, what does that look like?
Two lines that are parallel and do not intersect.
y=-2x-1
y=x+5
(-2,3)
-3x - 3y = 3
y = -5x - 17
(-4, 3)
You and a friend go to Tacos Galore for lunch. You order two soft tacos and three burritos and your total bill is $13.00. Your friend's bill is $12.00 for four soft tacos and two burritos. How much do soft tacos cost? How much do burritos cost?
Let x = soft tacos Let y = burritos
Write equations to represent you and your friend, then use the equations to solve for x and y.
You: 2x+3y=13
Friend: 4x +2y= 12x
x= $1.25 y=$3.50
7x + 5y = 8
7x + 7y = 8
(8/7,0)
It is possible to have infinitely many solutions to a system of linear equations?
a) When solving by graphing what would that look like?
b) When eliminating what would happen?
Yes it is possible.
a) They would graph as the same line.
b) You would eliminate both variables and the constants and have 0=0.