Download Solving Systems of Equations

Section 7-1 Solve Systems by Graphing
SPI 23D: select the system of equations that could be used to solve a given real-world
problem
Objective:
• Solve systems of linear equations by graphing
• Slope-intercept form of a linear equation: y = mx + b
• Standard form of a linear equation: Ax + By = C
Systems of Linear Equations:
• two or more linear equations together
Solving Systems of Equations:
• means finding a solution to both equations (an ordered pair) that
makes both equations true
Recall Graphing Slope-Intercept Form of a Linear Equation
Graph y = - 1 x – 2
2
Y
1. Plot y-intercept
2. From known point, plot
slope.
3. Connect the 2 points
with a line.
0
X
Recall Graphing Standard Form of a Linear Equation
Graph the equation -5x – 2y = 10.
Step 1. Find the x-intercept.
-5x – 2(0) = 10
-5x = 10
x = -2
(-2, 0)
Step 2. Find the y-intercept.
-5(0) – 2y = 10
-2y = 10
y = -5
(0, -5)
Step 3. Plot both ordered pair and draw the line.
Solve Systems of Equations
Three Methods of solving Systems of Equations:
• Solve by Graphing
• Solve by Substitution
• Solve by Elimination
Solve a System of Equations by Graphing
Solve by graphing.
y=x+5
y = -4x
1. Graph the equations on the
same coordinate plane.
0
2. Write the ordered pair where
the lines intersect.
(-1, 4)
Solution that will make both equations true.
Solve Systems of Equations
Life Science. You are testing two fertilizers on a plant which grow
under identical conditions. The equation H(d) = 4d + 6 models the
growth rate of the first plant and the equation H(d) = 2d + 10
models the growth rate of the second plant. In the equations, d
represents the number of days it takes the plants to grow a certain
height, H(d).
1. Model the equations by graphing
on the same coordinate plane.
2. After how many days will the
plants be the same height?
2 days
3. What will their height be?
14 cm
Number of Solutions to a System of Equations
A System of Equations can have:
• One Solution
• No Solution
• Infinitely Many Solutions
One Solution
• different slopes
• lines intersect
No Solution
Infinitely Many
• same slope
• same slope
• lines are parallel
• same y-intercept
• different y-intercepts