Graphing Systems of Equations
When two lines on the graph are parallel , what solution is that?
It’s a No solution or The system has no solution
What’s the first step in substitution?
The first step is to solve one equation for on variable
If both variables cancel , what does that mean?
it means there’s no solution to the problem.
What if you multiplied both equations and it turns to be the same answer? What does that mean?
It means theres many solutions or As we call it, Infinitely solutions
True or false : The solution to a system of inequalities is always a line.
False. Because its a region.
If two lines on the graph overlap each other , what does that mean?
It means that there is Infinite solution.
Solve : y = 2x. and x + y = 12.
X + 2x = 12 > 3x = 12 > x == 4, y = 8.
so the answer is ( 4.8)
Solve. x + y = 10 And x - y = 4.
( x + y ) + ( x - y ) = 2x = 14 which equals to 7.
True/False. you can use elimination if the coefficients match.
false because we can multiply to make them match.
Graph. Y > -3/4x + 4
y > 1/2x - 1. ( what points are on the graph)
(4,1)
Graph : y = 2x - 3 and y = -x + 3.
where does the line intersect?
It Intersect at ( 2 , 1)
Solve : y = -x + 5. And 2x + y =7.
2x + (x + 5) = 7 , x +5 = 7
Solve. 2x + y = 9 and - 2x + y = 1.
x equals to 2. Y equals to 5. ( x = 2 , y = 5)
True/false. When the final elimination is ( 0 = 4) , does it mean there’s no solution?
True.
Graph. 2x + 3y ~> -9
X ~< -3 ( what points are on the graph)
(-3,0) or ( -3,-1)
Graph. Y = -2x + 6 , x + y = 4.
( 2,2)
Solve. y = 2x - 5 , 3x + y = 10.
x will equal to 3 , x will equal to 1 ( 3,1)
Solve. 1/2x + y = 5. and 1/2x - y = 1.
x = 6. , y = 2.
Solve. -9x + 3y = 27
-3x + 4y =27
( -1, 6): x is -1 , y is 6.
Graph . Y ~> 1/3 x + 3
Y > 2x-2. ( what points are on graph)
( 3, 4 )
Create a system with one solution. : must show explanation and answer. ( must be different examples from mine)
Example : i take these two equations ( 5x + 2y =12 and 3x - y = 0) and which i put into Desmos and they intersect at (1.09 , 3.2). I know it’s one solution since the graph intersects and gives me one pair.
Solve. X = 2y + 1 , 3x - y = 14.
x will equal to 5.4 or 27/5. y will equal to 2.2 or 11/5.
Solve. 5x + 3y = 24, 5x - 2y = 9.
y = 3, x = 3 ( 3,3)
Solve. 10x + 12y = -26
-6x + 6y = -24
( 1, -3): x is 1 , y is -3
Graph. -x + 3y ~< -6
-5 + 3y ~< 6 ( what points are on the graph )
(0,-2)