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Algebra
Chapter 7
Vocabulary
System of linear equations- two or more
linear equations in the same variables.
Solution of a system of linear
equations- an ordered pair (x, y) that
satisfies each equation.
Re-teach
Solving a linear system using graph- and –check
1) Write the equation in a form so it is easy to
graph.
2) Graph both equations.
3) Estimate the points (x,y) for intersection.
4) Check algebraically by substituting into each
equation.
Practice
Graph the linear system, then decide if the
ordered pair is a solution.
1. x + y = -2
(-3, 1)
2x – 3y = -9
2. –x + y = - 2 (4, -2)
2x + y = 10
3. x + 3y = 15
4x + y = 6
(3, -6)
Re-teach
Solving systems of equations by substitution
1) Solve one of the equations for one of its
variables.
2) Substitute the revised Expression in for the
other equation.
3) Solve the equation for the variable.
4) Substitute in the solution for one of the
variables into the original equation.
5) Write the solution in an ordered pair.
Re-teach
Solving systems of equations by substitution
-x + y = 1
2x + y = -2
1) Solve one of the equations for one of its
variables.
-x + y = 1
+x
+x
Y=x+1
2x + y = -2
Re-teach
Solving systems of equations by substitution
2) Substitute the revised Expression in for
the other equation.
Y=x+1
2x + y = -2
2x + x + 1 = -2
Re-teach
Solving systems of equations by
substitution
3) Solve the equation for the variable.
2x + x + 1 = -2
3x + 1 = -2
3x = -3
X = -1
Re-teach
Solving systems of equations by substitution
4) Substitute in the solution for one of the
variables into the original equation.
-x + y = 1
2x + y = -2
X = -1
2(-1) + y = -2
-2 + y = -2
Y=0
Re-teach
Solving systems of equations by substitution
5) Write the solution in an ordered pair.
X = -1
Y=0
(-1, 0)
Practice
1) 2x + 2y = 3
x – 4y = -1
2) –x + y = 5
½x + y = 8
3) 3x + y = 3
7x + 2y = 1
Vocabulary
Linear Combination- an equation obtained
by adding one of ht equations to the
other equation.
A linear combination is often known as
solving systems of equations through
elimination.
Re-teach
Solving linear systems by linear combinations
1) Arrange the equations with like terms in
columns.
2) Multiply one or both of the equations to
obtain an opposite variable.
3) Add/Subtract the terms from each
column to get the value of the variable.
4) Substitute the value into the original
equations.
5) Write the solution in an ordered pair.
Re-teach
Solving linear systems by linear combinations
1) Arrange the equations with like terms in
columns.
3x + 2y = 44
5y + x = 11
3x + 2y = 44
X + 5y = 11
Re-teach
Solving linear systems by linear combinations
2) Multiply one or both of the equations to
obtain an opposite variable.
3x + 2y = 44
-3(X + 5y = 11)
3x + 2y = 44
-3x -15y = -33
Re-teach
Solving linear systems by linear combinations
3) Add/Subtract then divide the terms from
each column to get the value of one variable.
3x + 2y = 44
-3x -15y = -33
-11y = 11
Y = -1
Re-teach
Solving linear systems by linear combinations
4) Substitute the value into the original
equation.
Y = -1
3x + 2y = 44
5y + x = 11
5(-1) + x = 11
-5 + x = 11
X = 16
Re-teach
Solving linear systems by linear
combinations
5) Write the solution as an ordered Pair.
Y = -1
X = 16
(16, -1)
Re-teach
One solution
(system will have perpendicular slopes)
No solutions (system will have parallel slopes)
Infinite solutions
(system will be the same or
equal 0 = 0)
Practice
Determine the type of results from each
system.
1) 3x + y = -1
-9x – 3y = 3
2) X – 2y = 5
-2x + 4y = 2
3) 2x + y = 4
4x – 2y = 0
Vocabulary
System of linear inequalities- two or
more linear inequalities.
Solution- ordered pair of the inequality in
each system.
Graph of linear inequalities- graph of all
solutions of the system.
Warm Up
When is a line dotted?
When is a line solid?
How do we determine which way to shade
a graph?
Re-teach
Triangular Solution
y<2
x ≥ -1
y>x–2
1) Graph each system on the same plane.
2) The overlap is the intersection of the
graphs.
3) After graphing pick a point, check to see
if the point is a solution algebraically.
Re-teach
Solution between parallel lines
Y<3
Y>1
1) Graph the equations.
2) Determine the overlapping shaded area.
Re-teach
Quadrilateral Solution Region
x≥0
Y≥0
Y≤2
Y ≤ -½x + 3
1) Graph the system of linear inequalities.
2) Label each intersecting point.
3) Shade the region inside the intersecting
points.
Practice
Graph and determine the types of solutions
from each system.
1) 2x + y < 4
-2x + y ≤ 4
2) 2x + y ≥ -4
x – 2y < 4
3) 2x + y ≤ 4
2x + y ≥ - 4