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Published byJack Wiley Modified over 2 years ago

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Solving Systems of Equations Using Substitution Students will solve systems of equations using substitution.

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FHSSystems of Equations2 Why Not Use Graphing? This graph shows a system of linear equations. As you can see, determining the solution from the graph is not easy. But, you can use the substitution method to find an exact solution. In substitution, you solve one equation for one variable and then substitute this expression into the other equation.

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FHSSystems of Equations3 Using Substitution – Example 1 Use substitution to solve the system of equations. Step 1: Solve one equation for one variable. The first equation is already solved for y : y = x – 1 Step 2: Substitute the expression into the other equation.

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FHSSystems of Equations4 Example 1 (cont.) Step 3: Substitute the x-value into one of the original equations to solve for y. x + y = 7 x + (x – 1) = 7 2x – 1 = 7 x = 4 Substitute (x –1) for y in the other equation. Combine like terms. y = x – 1 y = (4) – 1 y = 3 Substitute x = 4. The solution is the ordered pair (4, 3).

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FHSSystems of Equations5 Example 2 Use substitution to solve the system of equations. Step 1: Solve one equation for one variable. The first equation is already solved for y : y = 2x – 1 Step 2: Substitute the expression into the other equation.

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FHSSystems of Equations6 Example 2 (cont.) Step 3: Substitute the x-value into one of the original equations to solve for y. 3x + 2y = 26 3x + 2(2x – 1) = 26 7x – 2 = 26 x = 4 Substitute (x –1) for y in the other equation. Combine like terms. y = 2x – 1 y = 2(4) – 1 y = 7 Substitute x = 4. The solution is the ordered pair (4, 7).

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