Assignment: Page 87 #8-16 even, 17, 23, 24, 30

Section 3.1: systems of equations Learning Target: I can solve systems of equations using various methods.

Solving systems by graphing Step 1: Get each linear equation in slope-intercept form. Recall slope-intercept form! Step 2: Graph each linear equation on the same set of axes. Step 3: Identify the solution (intersection of the linear equations)

Consistent/inconsistent and independent/dependent Consistent: at least one solution in the system Inconsistent: no solution (what does this graph look like?) Independent: Exactly one solution Dependent: Infinitely many solutions

Solve the system by graphing: 2𝑥−𝑦=−1 2𝑦+5𝑥=−16 Example 1:

Solving systems by substitution: In order to solve a system of equations by substitution, one of the equations must have a variable isolated on one side of the equal sign. After one equation is written in this manner, substitute the function into the other linear equation and solve for the variable in the equation. After determining the value, substitute that value (should be a constant value) into the other equation to determine the remaining value.

Example 2: Jeffrey has a computer support business. He estimates the cost to run his business is modeled by the function 𝑦=48𝑥+500, where 𝑥 is the number of customers. He also estimates his income can be represented by the function 𝑦=65𝑥−145, where 𝑥 is the number of customers. How many customers will Jeffrey need in order to break even? What will his profit be if he has 60 customers? Step 1: Substitute 48𝑥+500 into the other function for 𝑦. (48𝑥+500 = 65𝑥−145). Solve for x. Step 2: Jeffrey needs _____ customers to break even. (This is the x value you just found) Step 3: To determine the profit for 60 customers, substitute 60 into each equation. Profit is modeled by the formula PROFIT=INCOME-COST. Jeffrey’s profit for 60 customers is __________.

Example 3: Solve the system of equations by substitution: 9𝑦+3𝑥=18 −3𝑦−𝑥=−6