P.o.D. – Solve each inequality.
1.) 14<2x-6 and 2x-6<50
or {14<2x-6<50}
2.) x-6<-12 or 2x-4>10
3.) 13<y+3(-4y+8)
1.) 14+6<2x<50+6  20<2x<56 
10<x<28
2.)
X<-12+6
X<-6
2x>10+4
2x>14
X<-6 or x>7
3.)13<y-12y+24  13<-11y+24 
-11<-11y  1>y or y<1
5-2: Solving Systems Using Tables,
Graphs, or a CAS (Computerized
Algebraic Solver)
Learning Target: be able to recognize
properties of systems of equations; use
systems of two linear equations to solve
real-world problems; estimate solutions
to systems by graphing.
System:
A set of two or more equations.
Solution Set of a System:
The intersection of the two equations.
Find Solutions Graphically:
1. Put the equations in slope-intercept
form. (Solve for y)
2. Graph the two equations.
3. Find the point of intersection.
𝑦 = 3𝑥 + 2
EX: Solve the system {
𝑦 = 2𝑥 − 4
Step 1: Put each equation in slopeintercept (y=mx+b) form.
Step 2: Graph the two equations.
Step 3: Find the point of intersection.
The solution is (-6,-16).
EX: Fred wants to enclose a 400 square
meter rectangular garden with 70 meters
of fencing. To do this, he must use one
side of his barn as a side of the garden.
What can the dimensions of the garden
be?
Barn
Y
x
Let x+2y=70 and xy=400.
Step 1: Solve both equations for y.
x+2y=70
xy=400
2y=70-x
y=400/x
Y=(70-x)/2
Step 2: Graph the equations.
Step 3: Find the point(s) of intersection
Because x and y must be positive, we
only want to examine Quadrant I. The
solutions (x,y) are near (14,28) and
(56,7). Thus, the dimensions of the
garden should be 56 by 7 or 14 by 28.
𝑥𝑦 = 30
EX: Solve the system {
𝑥−𝑦=1
Step 1: Solve each equation for y.
xy=30
x-y=1
y=30/x
-y=1-x
y=x-1
Step 2: Graph each equation.
Step 3: Find the point(s) of intersection.
(-5,-6) and (6,5)
We can also find solutions to a system
using the TABLE.
- We simply look for where Y1 and Y2
have the same value.
Do the following on your own. Solve.
3
𝑦 = 𝑥+1
2
1.) {
𝑦 = 𝑥2
𝑦=
10
𝑥
2.) {
2𝑥 − 3𝑦 = 18
1.) (-0.5, 0.25), (2,4)
2.) (-1.4,-6.9), (10.4, .96)
EX: Have a student come to the board to
𝑦 = −2𝑥 + 1
solve the system
−3𝑥 + 𝑦 = −6
Set the two equations equal to y.
Y= -2x+1 and y=3x-6
(1.4, -1.8)
EX: To make yearbooks, it costs the
school $8 per yearbook and a $5000 setup fee. We sell the yearbooks for $50
each. How many yearbooks must we sell
in order to break even?
Set up an equation for cost and another
for revenue.
Y=8x+5000 {cost}
Y=50x {revenue}
Graph the two equations. [X axis: 0 to
200; Y axis: 0 to 10,000]
We need to sell 120 yearbooks to begin
making a profit.
Upon completion of this lesson, you
should be able to:
1. Set equations equal to y.
2. Graph multiple equations and find
their point(s) of intersection using a
graph (calculator).
3. Model real-world situations using
systems of equations.
For more information, visit
http://www.purplemath.com/modules/systlin2.htm
HW Pg. 310 4-21