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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: ___= ____