Download solving systems of linear equations graphically

TOOLKIT: SOLVING SYSTEMS OF LINEAR EQUATIONS GRAPHICALLY
Two or more equations considered together are called a system of equations. The following
example is a system of two linear equations with two variables.
Solving Systems of Equations by Graphing on Paper
The solution will be a point (x, y) on the graph.
Step 1: Plot the y-intercept of the 1st equation and
use the slope to draw the graph of the line.
Step 2: Plot the y-intercept of the 2nd equation and
use the slope to draw the graph of the line.
Step 3: Find the intersection(crossing point) of
the two lines on the graph.
Step 4: Write the ordered pair (x, y) for the solution.
Solve the following system of equations by graphing.
Example 1:
LineA : y =
1
3
x+4
LineB : y = −6 + 2x
Solution:
Example 2:
LineA : y = −2x − 3
LineB : y = 6 −
Solution:
1
2
x
Solving Systems of Inequalities by Graphing on Paper
The solution will be a shaded section of the graph.
Step 1: Graph the 1st equation, making sure it’s the correct
type of line. Shade lightly.
Step 2: Graph the 2nd equation, making sure it’s the
correct type of line. Shade lightly.
Step 3: Find the intersection(overlapping shaded sections)
Step 4: Shade the overlapping part of the graph darkly.
Example: Solve the following system of equations by graphing.
Line A : y > 8 − 3x
Line B : y ≥
1
2
x −6
IM 1
Investigation 3.3.3 Day 1
Name
Solve each of the following systems of equations by graphing. Make sure to draw lines accurately.
For the solution give the point of intersection as an ordered pair (x, y).
y = x + 6 and y = −2x − 6
1)
2)
Solution:
Solution:
3)
4)
Solution:
Solution:
9
2
y = − x + 5 and y = − x − 2
5
5
Solve each of the following systems of inequalities by graphing. Make sure to draw lines accurately.
For the solution shade the overlapping part of the graph darker than the rest.
5)
y ≤ −4 +
3
x and y ≥ 10 − 2x
2
6)
7)
1
3
y > − x + 8 and y < x + 4
4
4
8)
y>
1
x - 7 and y > −2x + 8
2