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
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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