Practice solving systems by graphing 1.)2.) 2x + 5y = –5 x + 3y = 3.

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Practice solving systems by graphing 1.)2.) 2x + 5y = –5 x + 3y = 3

Solving systems of linear equations by substitution. Solve for your second answer. Now you have x and y. Yea! You got one answer now take that answer and plug it back into step 1. Solve the second equation. The new equation will only have one variable. Solve by combining like terms adding, subt. Mult., and dividing. Substitute the expression you solved for in step 1 into the other equation. Whichever variable you solved for will be removed. It will be replaced with the expression you got. Solve One equation for one variable. Just like solving for y in graphing method.You can chose to solve for x or y.

EXAMPLE 1 Use the substitution method Solve the system using the substitution method. 2x + 5y = –5 x + 3y = 3 Equation 1 Equation 2 SOLUTION STEP 1 Solve Equation 2 for x. x = –3y + 3 Revised Equation 2 x + 3y = 3 -3y -3y

EXAMPLE 1 Use the substitution method STEP 2 Substitute the expression for x into Equation 1 and solve for y. 2x +5y = –5 2(–3y + 3) + 5y = –5 y = 11 Write Equation 1. Substitute –3y + 3 for x. Solve for y. STEP 3 Substitute the value of y into revised Equation 2 and solve for x. x = –3y + 3 x = –3(11) + 3 x = –30 Write revised Equation 2. Substitute 11 for y. Simplify. -6y y = -5 -y +6 = -5 -y = -11 STEP 4 STEP 5

EXAMPLE 1 Use the substitution method CHECK Check the solution by substituting into the original equations. 2(–30) + 5(11) –5 = ? Substitute for x and y. = ? –30 + 3(11) 3 Solution checks. 3 = 3 –5 = –5 The solution is (– 30, 11). ANSWER

EXAMPLE 2 Use the substitution method Solve the system using the substitution method. 3x - y = 2 6x + 3y = 14 Equation 1 Equation 2 SOLUTION STEP 1 Solve Equation 1 for y. y = 3x – 2 Revised Equation 1 3x - y = 2 -3x -3x -y = 2 – 3x This is what happens if you don’t do your math

EXAMPLE 2 Use the substitution method STEP 2 Substitute the expression for y into Equation 2 and solve for x. 6x +3y = 14 6x + 3(3x – 2) = 14 x = 4/3 Write Equation 2. Substitute 3x – 2 for y. Solve for y. STEP 3 Substitute the value of y into revised Equation 2 and solve for x. y = 3x – 2 y = 3(4/3) – 2 y = 2 Write revised Equation 1. Substitute 4/3 for x. Simplify. 6x + 9x – 6 = 14 15x – 6 = 14 15x = 20 STEP 4 STEP 5 Distribute, combine like terms, and solve.

EXAMPLE 3 Use the substitution method Solve the system using the substitution method. x - 2y = 4 3x - 6y = 8 Equation 1 Equation 2 SOLUTION STEP 1 Solve Equation 1 for x. x = 2y + 4 Revised Equation 1 x - 2y = 4 +2y +2y

EXAMPLE 3 Use the substitution method STEP 2 Substitute the expression for x into Equation 2 and solve for y. 3x - 6y = 8 3(2y + 4) - 6y = 8 The y canceled out Write Equation 2. Substitute 2y + 4 for x. Solve for y. STEP 3 6y y = 8 12 = 8 When this happens and your final answer is false 12 ≠ 8 the answer is NO Solution. What if the final answer had been true? The answer would have been infinite solutions.

You try solving by substitution. 3.)4.)