CCGPS Coordinate Algebra
UNIT QUESTION: How do I justify
and solve the solution to a system of
equations or inequalities?
Standard: MCC9-12.A.REI.1, 3, 5, 6, and 12
Today’s Question:
When is it better to use substitution
than elimination for solving systems?
Standard: MCC9-12.A.REI.6
Warm-up
Solve and graph each inequality
1. 7x < 21
2. 30 < 5k
3. -2n > -50
4.
𝑦
5
> -20


1.
2.
3.
Make sure each equation is in
slope-intercept form: y = mx + b.
Graph each equation on the
same graph paper.
The point where the lines intersect
is the solution. If they don’t intersect then
there’s no solution.
4.
Check your solution algebraically.
1
𝑦 = 𝑥+3
2
y=
3
𝑥
2
+1
Solution:
(2, 4)
2 x  2 y  8
2 x  2y  4
Solution:
(-1, 3)
y  2 x  5
y  2 x  1
yes
Solution
x  y  2
2 x  3 y  9
Solution:
(-3, 1)
y5
2x  y  1
Solution:
(-2, 5)
1) One
solution
2) No solution
3) Infinitely many
 If
the lines have the same y-intercept b, and the
same slope m, then the system has infinitely
many solutions.
 If
the lines have the same slope m, but different
y-intercepts b, the system has no solution.
 If
the lines have different slopes m, the system
has one solution.
Warm-Up 9/20/13
Solve each equation for y.
1. 2x + 3y = 6
2. -5x + 4y = 8
3. 3x – 4y + 12 = 0


1.
2.
3.
4.
5.
One equation will have either x or y by itself, or
can be solved for x or y easily.
Substitute the expression from Step 1 into the other
equation and solve for the other variable.
Substitute the value from Step 2 into the equation
from Step 1 and solve.
Your solution is the ordered pair formed by x & y.
Check the solution in both of the original equations.
1. y  6 x  11
 2 x  3y  7
2. 2 x  3 y  1
y  x 1
3. y  3 x  5
5 x  4y  3
4.  3 x  3y  3
y  5 x  17
5. y  2
4 x  3y  18
6. y  5 x  7
 3 x  2 y  12


Graphing and Substitution WS