Question

1. identify the error made in the given solution

2. fix the error and determine the correct solution

Answer 1

Hello !

1. System of equation

`3x + 2y = 10\\4x - y = 6`

2. The substitution method

We will use the substitution method.

1. We want to isolate y (isolating y is easier than isolating x) :

`4x - y = 6\\y = -6 + 4x`

2. We replace y in the 1st expression :

`3x + 2(-6 + 4x) = 10\\`

3. Now we solve the equation since we only have x

3.1 Solve x

`3x + 8x - 12 = 10\\11x - 12 = 10\\11x - 12 + 12 = 10 + 12\\11x = 22\\x = 22/11\\\boxed{x = 2}`

3.2 Solve y

`4*2 - y = 6\\8 - y = 6\\8 - y - 8 = 6 - 8\\-y = -2\\\boxed{y = 2}`

Have a good day !

Answer 2

The substitution step is incorrect.

x = 2; y = 2

Explanation:

The equation 4x - y = 6 is correctly solved for y as

y = 4x - 6.

The substitution method is being used. Once you solve one equation for one variable, you must substitute what that variable equals into the other equation. In this case, it was substituted into the same equation.

Here is the correct substitution step.

Substitute:

3x + 2(4x - 6) = 10

3x + 8x - 12 = 10

11x = 22

x = 2

Now substitute 2 for x in the 1st original equation:

3(2) + 2y = 10

6 + 2y = 10

2y = 4

y = 2

Answer: x = 2; y = 2