Methods to Solving Systems of Equations

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1 Methods to Solving Systems of Equations
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2 Graphing Substitution Elimination
Methods to Solving Systems of Equations

3 Graphing Steps: Solve each equation for y (slope-intercept form).
Graph both equations using the slope-intercept method. Observe the graph and identify the solution (point of intersection). 1 Solution - Consistent Independent Infinitely Many Solutions – Consistent Dependent No Solution – Inconsistent

4 Graphing Example 𝑦=−6𝑥 −3 𝑦+𝑥=2 𝑦+𝑥=2 2. 𝑦=−𝑥+2
𝑦+𝑥= 𝑦=−𝑥+2 3. The solution is (-1 , 3) This system of equations is consistent and independent

5 Substitution Steps: Solve one of the equations for one of its variables. Substitute the expression from Step 1 into the other equation. Example: Revised Equation

6 Substitution Example: Steps:
Solve the equation from step 2 for the other variable. Substitute the value from Step 3 into the revised equation from step 1 and solve. Write your final answer as an ordered pair. Solution is ( 1, 1 )

7 Elimination Steps: Write your equations so that the corresponding variables are aligned. Check to see if the same variable has the same coefficient. Multiply or divide to make the coefficients the same value, but different signs. Add the revised equations from Step 3 to eliminate one of the variables. Solve the resulting equation from Step 4 Substitute the value obtained in Step 5 into either of the original equations and solve for the other variable. Write the solution as an ordered pair.

8 Elimination Example Corresponding variables are already lined up.
𝑥 + 𝑦=1 2𝑥 −3𝑦=12 Corresponding variables are already lined up. Neither variable has the same coefficient with signs that differ. Let’s multiply the first equation by −2: −2(𝑥+𝑦=1) Resulting equation: −2𝑥−2𝑦=−2 Add the revised equations. −2𝑥−2𝑦=−2 2𝑥−3𝑦=12 Solve the equation from step 4. −5𝑦=10 −5𝑦 −5 = 10 −5 𝑦=−2

9 Elimination Example 𝑥 + 𝑦=1 2𝑥 −3𝑦=12 Substitute your answer from step 5 into the first equation and solve for x. 𝑥+𝑦=1 𝑥+−2=1 𝑥=3 Write your answer as an ordered pair. (3, -2)