EXAMPLE 1 Use the substitution method Solve the

EXAMPLE 1 Use the substitution method Solve the linear system: y = 3 x + 2 Equation 1 x + 2 y = 11 Equation 2 SOLUTION STEP 1 Solve for y. Equation 1 is already solved for y.

EXAMPLE 1 Use the substitution method STEP 2 Substitute 3 x + 2 for y in Equation 2 and solve for x. x + 2 y = 11 x + 2(3 x + 2) = 11 7 x + 4 = 11 7 x = 7 x=1 Write Equation 2. Substitute 3 x + 2 for y. Simplify. Subtract 4 from each side. Divide each side by 7.

EXAMPLE 1 Use the substitution method STEP 3 Substitute 1 for x in the original Equation 1 to find the value of y. y = 3 x + 2 = 3(1) + 2 = 3 + 2 = 5 ANSWER The solution is (1, 5).

EXAMPLE 1 Use the substitution method GUIDED PRACTICE CHECK Substitute 1 for x and 5 for y in each of the original equations. y = 3 x + 2 5 =? 3(1) + 2 5 = 5 x + 2 y = 11 1 + 2 (5) =? 11 11 = 11

EXAMPLE 2 Use the substitution method Solve the linear system: x – 2 y = – 6 4 x + 6 y = 4 Equation 1 Equation 2 SOLUTION STEP 1 Solve Equation 1 for x. x – 2 y = – 6 x = 2 y – 6 Write original Equation 1. Revised Equation 1

EXAMPLE 2 Use the substitution method STEP 2 Substitute 2 y – 6 for x in Equation 2 and solve for y. 4 x + 6 y = 4 4(2 y – 6) + 6 y = 4 8 y – 24 + 6 y = 4 14 y – 24 = 4 14 y = 28 y=2 Write Equation 2. Substitute 2 y – 6 for x. Distributive property Simplify. Add 24 to each side. Divide each side by 14.

EXAMPLE 2 Use the substitution method STEP 3 Substitute 2 for y in the revised Equation 1 to find the value of x. Revised Equation 1 x = 2 y – 6 x = 2(2) – 6 Substitute 2 for y. x = – 2 Simplify. ANSWER The solution is (– 2, 2).

EXAMPLE 2 Use the substitution method GUIDED PRACTICE CHECK Substitute – 2 for x and 2 for y in each of the original equations. Equation 1 Equation 2 x – 2 y = – 6 4 x + 6 y = 4 ? – 2(2) = – 6 ? 4(– 2) + 6 (2) = 4 – 6 = – 6 4 = 4

EXAMPLE 1 for Examples 1 and 2 Use the substitution method GUIDED PRACTICE Solve the linear system using the substitution method. 1. y = 2 x + 5 3 x + y = 10 ANSWER (1, 7)

EXAMPLE 2 for Examples 1 and 2 Use the substitution method GUIDED PRACTICE Solve the linear system using the substitution method. 2. x– y= 3 x + 2 y = – 6 ANSWER (0, – 3)

EXAMPLE 2 for Examples 1 and 2 Use the substitution method GUIDED PRACTICE Solve the linear system using the substitution method. 3. 3 x + y = – 7 – 2 x + 4 y = 0 ANSWER (– 2, – 1)