Solving Systems of Equations Using Substitution Connections - Tuesday, November 9 Unit D.3 Solving Systems of Equations Using Substitution Students will solve systems of equations using substitution. Unit D.3 - Soving Systems Using Substitution

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. FHS Systems of Equations

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. FHS Systems of Equations

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

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. FHS Systems of Equations

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