Download 4-2 Notes - Mr. Parrott`s Math Class

4-2 Notes: Solve a System of Equations by Substitution
Learning Targets: I Can…..
Previously Learned about this Topic:
●
Graph a line from two points, from slope intercept form, and given a slope and a point/y-intercept
●
Solve for y (transform into slope-intercept form)
8. When looking at a graph of two lines, I can determine whether there is 1 solution, no solution, or infinitely many
solutions.
9. When looking at two tables, I can determine whether there is 1 solution, no solution, or infinitely many
solutions.
New Learning:
11. Solve a system using Substitution: Meaning I can find plug one of my equations into the the other one and solve for
one variable.
Basic Algebraic Substitution:
1. Given the equation2𝑥 + 4𝑦 = 20, and 𝑦 = 2, use
substitution to find the value of x.
2. Given the equation2𝑥 + 4𝑦 = 20, and 𝑦 = 2𝑥, use
substitution to find the value of x.
Solution: _________________________________
Solution: ____________________________________
3. Given the equation2𝑥 + 3𝑦 = 20, and 𝑥 = 7, use
substitution to find the value of x.
4. Given the equation2𝑥 + 4𝑦 = 20, and 𝑥 = 3𝑦, use
substitution to find the value of x.
Solution: __________________________________
Solution: _________________________________
4-2 Notes: Solve a System of Equations by Substitution
Example: Solve each system of equations by substitution.
5. 𝑦 = 3𝑥
and 𝑥 + 𝑦 = 8
6. 2𝑥 + 𝑦 = 9
Solution: ________________________
Substitute equation into equation:
and 𝑥 = −4𝑦 + 1
Solution: _______________________
Substitute number
value into equation:
Substitute equation into
equation:
Substitute number
value into equation:
# value: ___= ____
Number value: ___= ____
# value: ___= ____
Number value: ___= ____
7. 𝑥 − 4𝑦 = −4 and −2𝑥 − 4𝑦 = 20
Solution: ________________________
Solve one equation for a single
variable:
Substitute new equation into
equation:
Substitute number value into
equation:
Equation: __________________
Number value: ___= ____
# value: ___= ____
4-2 Notes: Solve a System of Equations by Substitution
8. 2𝑥 − 𝑦 = 1 and 4𝑥 − 2𝑦 = 2
Solution: ____________
Solve one equation for a single
variable:
Substitute new equation into
equation:
Substitute number value into
equation:
Equation: __________________
Number value: ___= ____
# value: ___= ____
Special Case!!!
9. 𝑦 = 4𝑥 + 2
and 𝑦 = 5𝑥 + 6
10. 𝑦 = −6𝑥 − 4 and 𝑦 = −6𝑥 + 12
Solution: _____________
Substitute equation into equation:
Solution: _____________
Substitute number
value into equation:
# value: ___= ____
Number value: ___= ____