Bell RingerSolve for x.
2x – 5 = 35 – 18x
Today’s LEQ:How do you solve a system of equations by substitution?
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)
Solving Systems of Equations by Substitution – Part 1
Steps
1.) _____________ an equation for either x or y. 2.) ________________________ your expression
into the _______________ equation to find the value of x or y.
3.) ________________________ your value to find
the ______________ missing value of x or y.
Solve
Substituteother
Substituteother
Example
y = -x + 10
y = 2x + 1Steps
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
1.) _____________ an equation for either x or y. 2.) ________________________ your expression
into the _______________ equation to find the value of x or y.
3.) ________________________ your value to find
the ______________ missing value of x or y.
Solve
Substituteother
Plug inother
Example
y = 2x – 2 3x + 2y = 38
Steps1.) 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 = -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?)