Chapter 7.3
 Objective
 Students
NCSCOS 4.03
will know how to solve a system
of equations using addition
 What
 Two
is a system of equations?
equations where we try and find
their intersection.
 What
are the possible solutions to a
system of equations?
• One solution – an ordered pair where the two
lines intersect
• No solution – the lines are parallel so they have
no points of intersection
• Infinitely many solutions – they are the same line
so every point on one line is the same as the
other line
 Example
1: Use addition to solve the
system of equations:
 To
solve a system of
equations we have to
eliminate one of the
variables
 If we were to add these together could
we eliminate one of the variables?
 Yes, the y’s add up to zero!
 We can add the equations together to
“get rid” of the y’s
 We
add the
equations
 x + 3x = 4x
 -3y + 3y = 0
 We don’t write 0y so
it goes away
 7 + 9 = 16
 Solve
for x
 Divide both sides by 4
4
is the x value in the
point where the two
lines intersect
 Once
you know x,
plug it into either
equation to find the
y value
 We’ll use the first
one
 Substitute
 Subtract
4 for x
4 from both
sides
 Divide
 -1
by -3
is the y value for
the point where the 2
lines intersect
 Example
1: Use addition to solve the
system of equations:
 The
solution to this
problem is the point
where they intersect
 The
answer is:
 Solve
the following system of equations
1. x – 2y = 4
2x + 2y = 2
2. x + 4y = 3
3x – 4y = -7
3. 2x – 5y = -4
4x + 5y = -8
4. -3x – 2y = 4
2x + 2y = -2
5. -6x + 4y = -10
2x – 4y = -2
 Solve
the following system of equations
1. x – 2y = 4
2x + 2y = 2
2. x + 4y = 3
3x – 4y = -7
3. 2x – 5y = -4
4x + 5y = -8
4. -3x – 2y = 4
2x + 2y = -2
5. -6x + 4y = -10
2x – 4y = -2
1. (2, -1) 2. (-1, 1)
3. (-2, 0) 4. (-2, 1)
5. (3, 2)
 Example
2: Solve the following system of
equations:
 Does
first?
• No!
it matter which variable I solve for
 This
problem we
will have to solve
for y first since the
x’s add up to zero
 Add the two
equations
 Divide by 3
 Plug
the y value
into either equation
 Solve for x
 Solve
the following system of equations:
1. -x + 3y = 7
2. -2x + 3y = 7
x + y = -1
2x – 4y = -3
3. -4x + 2y = 2
4x – 2y = 4
5. -2x + 3y = -2
2x – 6y = -4
4. 3x + 2y = 9
-3x – 8y = 3
 Solve
the following system of equations:
1. -x + 3y = 9
2. -2x + 3y = 8
x + y = -1
2x – 4y = -4
4. 3x + 2y = 8
3. -4x + 2y = 2
-3x – 8y = 4
4x – 2y = 4
1. (-3, 2)
5. -2x + 3y = -2
2x – 6y = -4
2. (-10, -4)
3. No Solution
4. (4, -2)
5. (4, 2)