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System of Equations
Transcript of System of Equations
5=y+x 5=2y+(y-10) 5=3y-10 15=3y __ __ 5=y 5=5+x x=0 3 3 Step 1: Substitute the variable that you know into the other equation. Step 2: Solve for the unknown
variable Step 3: Plug the answer you just found back into one of the equations and solve for the other variable Step 4: Put your answer in (x,y) format. (0,5) In this way of solving systems of equations, one variable is eliminated by adding or subtracting the equations. 2x+y=10
3y=15 __ __ 3 3 y=5 2x+5=10 -5 -5 2x=5 __ _ 2 2 x=2.5 Example: 2x+y=10
-2x+2y=5 3y=15 __ __ 3 3 y=5 2x+5=10 -5 -5 2x=5 __ _ 2 2 x=2.5 (2.5,5) Step 1: Cancel out the two variables that have the opposite coefficient.
Step 2: Solve for the remaining variable
Step 3: Plug the known variable back into either equation and solve
Step 4: Put answer in (x,y) format. To solve a system of equations graphically, graph both equations and see where they intersect. The intersection point is the solution. Example: 4x - 6y = 12
2x + 2y = 6 First Step: Get the equation into y=mx+b form Second Step: Graph the two lines and find out the point of intersection
Third Step: The point of intersection is your final answer. y=2/3x-2
y=-x+3 (3,0) Any Questions?