SOLVING SYSTEMS BY SUBSTITUTION The substitution method has 3 steps:
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| Example: Solve the linear system using the substitution method. 3x + 4y = -4 x + 2y = 2 Solution 1.) Solve Equation 2 for x. x + 2y = 2 x = -2y + 2 2.) Substitute the expression for x into Equation 1 and solve for y. 3x + 4y = -4 3(-2y + 2) + 4y = -4 y = 5 3.) Substitute the value of y into revised Equation 2 and solve for x. x = -2y + 2 x = -2(5) + 2 x = -8 The solution is (-8,5). CHECK the solution by substituting back into the original equations. 3x + 4y = -4 3(-8) + 4(5) =? -4 -4 = -4 x + 2y = 2 -8 + 2(5) =? 2 2 = 2 |
| Example: Solve the linear system using the substitution method. 4x - 2y = -1 3x - y = 8 Solution 1.) Solve Equation 2 for y. 3x - y = 8 y = 3x - 8 2.) Substitute the expression for y into Equation 1 and solve for x. 4x - 2y = -1 4x - 2(3x - 8) = -1 x = 17/2 3.) Substitute the value of x into revised Equation 2 and solve for y. y = 3x - 8 y = 3(17/2) - 8 y = 35/2 The solution is (17/2,35/2). CHECK the solution by substituting back into the original equations. 4x - 2y = -1 4(17/2) - 2(35/2) = -1 -1 = -1 3x - y = 8 3(17/2) - 35/2 = 8 8 = 8 |
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Problem: You want to burn 380 Calories during 40 minutes of exercise. You burn about 8 Calories per minute inline skating and 12 Calories per minute swimming. How long should you spend doing each activity? Y represents total minutes of swimming. X represents total minutes of skating. Your 1st Equation needs to be setup as follows. x + y = 40 This is because the variables represent the minutes spent on each activity and the sum of the minutes has to equal 40. Your 2nd Equation needs to be setup as follows. 8x + 12y = 380 This is because the numbers represent the total calories burned on skating and swimming. The goal calories burned is 380 so that is why it is the sum of the equation. Solution 1.) Solve Equation 1 for x just to make things easier. x + y = 40 x = -y + 40 2.) Substitute the expression for x into Equation 2 and solve for y. 8x + 12y = 380 8(-y + 40) + 12y = 380 y = 15 3.) Substitute the value of y into revised Equation 1 and solve for x. x = -y + 40 x = -15 + 40 x = 25 The solution is (25,15). CHECK the solution by substituting back into the original equations. x + y = 40 25 + 15 = 40 40 = 40 8x + 12y = 380 8(25) + 12(15) = 380 380 = 380 Since the solution checks that means you would have to spend 25 minutes skating and 15 minutes swimming to burn 380 calories in 40 minutes.
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