Algebra I –Wilsen
Unit 6: Systems of Equations
Day Nine
BLOCK 2
Solving Systems by Graphing
Remember: A system of equations is a set of 2 equations with 2 variables.
Example 1
y = –x – 2
y = 2x – 5
We have already learned to solve systems of equations using substitution and elimination.
Now we will learn to solve them by GRAPHING.
• Remember that each equation that includes x and y represents a line.
• If we graph both equations on
the same axes, we’ll get two
lines:
• The solution of the system of equations is the coordinates of the point where the two lines
intersect!
o Draw a point where the two lines intersect.
o What are the (x, y) coordinates of this point? ____________
o So, the final solution to the system of equations is:
x = ________, y = ________
o Check your answer by substituting the values of x and y into the original
equations.
Practice Problems:
Each graph below represents a system of equations. (Each line represents one equation.)
What is the solution to each system?
1.
2.
x = ______, y = ______
3.
x = ______, y = ______
4.
x = ______, y = ______
x = ______, y = ______
The “hard” part about solving systems of equations by graphing is that you have to graph
your equations yourself!
To solve a system of equations by graphing, follow these steps:
• Step 1: Make sure each equation is in “y = mx + b” format.
• Step 2: Graph both equations on the same axes.
• Step 3: The solution is the coordinates of the point where the two
lines intersect!
Example 2:
x+ y=5
2y = 4x –8
Step 1: Are both equations in “y = mx+b” format?
If not, put them into “y = mx + b” format.
x+y=5
2y = 4x – 8
Step 2: Graph both equations on the same axes. Use a ruler and draw your lines
CAREFULLY!!
Step 3: x = _____, y = _____
Don’t forget – you can check your answer!
Solve each system of equations by graphing. Follow these steps:
• Step 1: Make sure each equation is in “y = mx + b” format.
• Step 2: Graph both equations on the same axes. Use a ruler!!
• Step 3: The solution is the coordinates of the point where the two
lines intersect!
Remember, you can always check your answers!!
1.
y = 2x + 4
x + y = –5
x = _______, y = _______
2.
y=
1
x−3
2
x+y=3
x = _______, y = _______
3.
2x + y = 5
y = 3x + 5
x = _______, y = _______
4.
y=
1
2
x–3
–3x + y = –8
x = _______, y = _______
5.
y=x–4
1
2
x+y=2
x = _______, y = _______
6.
3x + y = 0
y=2–x
x = _______, y = _______