Question

Alejandro was asked to solve a system of linear equations by using the substitution method. What is the error in his work below? Step 1: 4y + x = 15 −9x + 5y = 20 Step 2: 4y + x = 15 x = 15 − 4y Step 3: 4y + x = 15 4y + (15 − 4y) = 15 4y + 15 − 4y = 15 15 = 15 There are infinitely many solutions to the system of linear equations

Answer 1

Y is 155/41 or 3 32/41

Answer 2

Step 1:
4y + x = 15
−9x + 5y = 20

Step 2: correct
4y + x = 15
x = 15 − 4y

Step 3: wrong
4y + x = 15
4y + (15 − 4y) = 15 wrong step
4y + 15 − 4y = 15
15 = 15
***once you have solved for a variable in one equation, you substitute it in the other equation

Corrected Step 3:
−9x + 5y = 20
-9(15 - 4y) + 5y= 20
(-9*15) + (-9*-4y) + 5y= 20
-135 + 36y + 5y= 20
-135 + 41y= 20
add 135 to both sides
41y= 155
divide both sides by 41
y= 155/41 or 3 32/41 or 3.78


ANSWER: The x value in step 2 should have been substituted in the opposite equation in step 3. The y solution would then be 155/41 or 3 32/41 or 3.78

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