Bell Ringer
Solve for x.
2x – 5 = 35 – 18x
We already know we can solve a system
of equations by graphing…
What might make graphing to solve a
system difficult?
Not a nice y-intercept, the lines may
not intersect at a definite (x,y)
Today’s LEQ:
How do you solve a system
of equations by substitution?
Solving Systems of Equations
by Substitution – Part 1
Steps
Solve an equation for either x or y.
1.) _____________
Substitute
2.) ________________________
your expression
into the _______________
equation to find the
other
value of x or y.
Substitute
3.) ________________________
your value to find
the ______________
missing value of x or y.
other
Example
y = -x + 10
y = 2x + 1
Steps
1.) Solve an equation for
either x or y.
2.) Substitute your
expression into the
other equation to find
the value of x or y.
3.) Plug in your value to
find the other missing
value of x or y.
Let’s do some more….
Find the solution to the system of equations by using
substitution:
1.
y = 3x + 5
y = -x + 13
Let’s do some more….
Find the solution to the system of equations by using
substitution:
2.
x = -y + 10
x = 2y + 1
Let’s do some more….
Find the solution to the system of equations by using
substitution:
3.
y = 2x
y = 5x – 33
Let’s do some more….
Find the solution to the system of equations by using
substitution:
4.
-3y = x
x = -y + 14
Quick Check
Solve the system.
2 + 3y = x
x = -2y - 8
Now.….
Help me solve the following equation for y.
2x – 8y = 24
Solving Systems of Equations
by Substitution – Part 2
Steps
Solve an equation for either x or y.
1.) _____________
Substitute
2.) ________________________
your expression
into the _______________
equation to find the
other
value of x or y.
Plug in
3.) ________________________
your value to find
the ______________
missing value of x or y.
other
Example
Steps
1.) Solve an equation for
either x or y.
2.) Substitute your
expression into the
other equation to find
the value of x or y.
3.) Plug in your value to
find the other missing
value of x or y.
y = 2x – 2
3x + 2y = 38
Let’s do some more….
Find the solution to the system of equations by using
substitution:
1.
y = -4x
12x + y = 48
Let’s do some more….
Find the solution to the system of equations by using
substitution:
2.
2x = 4y
x = 30 – 13y
Let’s do some more….
Find the solution to the system of
equations by using substitution:
3.
x + y = 1
15 – 8y = x
Let’s do some more….
Find the solution to the system of equations by using
substitution:
4.
6x = 2y
y = 4x – 4
Paper Quick Check
(Graded?)