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)
2)
3)
4)
Write the equation in a form so it is easy to graph.
Graph both equations.
Estimate the points (x,y) for intersection.
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
2x – 3y = -9
2. –x + y = - 2
2x + y = 10
3. x + 3y = 15
4x + y = 6
(-3, 1)
(4, -2)
(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