Lecture 2.2 graphs ii - solving simult.eqns graphically
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Transcript of Lecture 2.2 graphs ii - solving simult.eqns graphically
Solving simultaneous
equations graphically
y = 2x + 1y = 4 - x
Solve the simultaneous equations graphically.
The Question:
y = 2x + 1 y = 4 - x
Begin by constructing a table of values:
x
y
y = 2x + 1
-2 0 2 4
Use the equation to fill in the y value when x = -2
-3
Now fill in the rest of the table
1 5 9
y = 2x + 1 y = 4 - x
x
y
-2
-3
0
1
2
5
4
9
y = 2x + 1Use the table to draw the graph of the equation.
-4
-2
0
2
4
6
8
10
-3 -2 -1 0 1 2 3 4 5x
y
y = 2x + 1
y = 2x + 1 y = 4 - x Now construct a second table of values:
6 4 2
x
y
-2 0 2 4
0
Y = 4 - x
Plot this line on the axes you used earlier...
-4
-2
0
2
4
6
8
10
-3 -2 -1 0 1 2 3 4 5x
y
y = 2x + 1
y = 4 - x
The solution is where the 2 lines cross:
Read the x-value from the x-axis...1
Now read off the y-value...3
So the solution of y = 2x + 1 and y = 4 - x is...
x = 1 y = 3 and