Download 5.2.4 day 1

January 26, 2017
Learning Target:
Continue work with solving systems of equations
using the Equal Values Method when equations
are not in y-form and learn to identify systems that
represent the same line or parallel lines (that is,
systems that have infinitely many solutions or no
solution).
Focus Questions
• What is a solution to an equation? What does it look like?
• What is the growth pattern?
• What is the y-intercept?
January 26, 2017
C
Think, Ink, Pair, Share
You have been introduced to systems of linear equations that are used to represent various situations. You have used the
Equal Values Method to solve systems algebraically. Just as in linear equations you found that sometimes there were no
solutions or an infinite number of solutions, today you will discover how this same situation occurs for systems of
equations.
5-52. Sara has agreed to help with her younger sister’s science fair experiment. Her sister planted string beans in two pots. She is using a different fertilizer in
each pot to see which one will grow the tallest plant. Currently, plant A is 4
inch per day, while plant B is 9 inches tall and grows
inches tall and grows
inch per day. If the plants continue growing at these rates, in how many days
will the two plants be the same height? Which plant will be tallest in six weeks? Write a system of equations and solve.
January 26, 2017
Think, Ink, Pair, Share
C
5-53. Felipe applied for a job. The application process required him to take a test
of his math skills. One problem on the test was a system of equations, but one of
the equations not in y = mx + b form. The two equations are shown below.
3x + 2y = 9
y=
x-5
Work with your team to find a way to solve the equations using the Equal Values
Method. January 26, 2017
Vocab
Tool Kit
pg. 43
coefficient (numerical) A number multiplying a variable or product of variables. For
example, −7 is the coefficient of −7x.
constant A number that is not multiplied by a variable. In the expression 2x + 3(5 − 2x)
+ 8, the number 8 is a constant term. The number 3 is not a constant term,
because it is multiplied by a variable inside the parentheses.
solution The number or numbers that when substituted into an equation or inequality
make the equation or inequality true. For example, x = 4 is a solution to the
equation 3x − 2 = 10 because 3x − 2 equals 10 when x = 4
January 26, 2017
Solutions to a System of Equations
A solution to a system of equations gives a value for each variable that
makes both equations true. For example, when 4 is substituted for x and 5
is substituted for y in both equations at right, both equations are true. So
x = 4 and y = 5 or (4, 5) is a solution to this system of equations. When the
two equations are graphed, (4, 5) is the point of intersection.
System with one solution:
Some systems of equations have
one solution. When the lines are
graphed they intersect at one
point.
Some systems have no solution. Notice that the
Equal Values Method would yield 3 = 4 , which
is never true. When the lines are graphed, they
are parallel. Some systems have infinite solutions.
Notice that the Equal Values Method would
yield 0 = 0 , which is always true. When the
lines are graphed, they overlap.
intersecting lines
x − y = −1
2x − y = 3
System with no solutions:
parallel lines
x + y = 3
x + y = 4
System with infinite solutions:
coinciding lines
x + y = 3
2x + 2y = 6