Question

The work of a student to solve a set of equations is shown below: Equation 1: x + 2y = 10 Equation 2: 2x + 5y = 15 Step 1: −2(x + 2y) = −2(10) 2x + 5y = 15 Step 2: −2x − 4y = −10 2x + 5y = 15 Step 3: 1y = 5 Step 4: x + 2(1) = 10 Step 5: x = 8 In which step did the student first make an error?

Answer 1

 −2x − 4y = −10 2x + 5y = 15 

Answer 2

Step 2 has error and step 4 has error.

Explanation:

Here we can see that elimination method is applied to solve the system of equations for which -2 is multiplied both sides of equation first

-2(x+2y)=-2(10 which is correct

but in step 2

left side is -2x-4y and the right side is -10 which has to be -20 which makes this step wrong and this is the error made by student.

in Step 4 also ,value of the y has to be 5 but student plugged y =1 which is also error by student.

Correct solution is

-2x-4y= -20

2x+ 5y= 15

on adding ,we get

y = -5

plugging y =5 in equation x+2y= 10 ,we get x+2(-5) =10 ,we get x = 20

therefore (20,-5) is the solution