Question

If solve 3x + 2y = 12 and 2x – 3y = 18 using substitution method.

Answer 1

Answer:

x=72/13

y=30/-13

Step-by-step explanation:

By substitution method

Answer 2

As a result, the system of equations solution is x = 114/39 and y = -46/13.

As per the question given,

To solve the given system of equations using the substitution method, we can follow these steps:

1. Solve one equation for one variable in terms of the other variable.
2. Substitute this expression for the variable into the other equation.
3. Solve the resulting equation for the remaining variable.
4. Substitute the value found for the remaining variable into the expression from step 1 to find the value of the first variable.

Let's use this method to solve the system:

3x + 2y = 12 ...(1)

2x - 3y = 18 ...(2)

Solving equation (1) for x, we get:

3x = 12 - 2y

x = (12 - 2y)/3

Now, we can substitute this expression for x into equation (2):

2((12 - 2y)/3) - 3y = 18

Simplifying this equation, we get:

8 - 4y - 9y = 54

-13y = 46

y = -46/13

We have found the value of y. Now, we can substitute this value into the expression for x that we found earlier:

x = (12 - 2y)/3

x = (12 - 2(-46/13))/3

x = 114/39

Therefore, the solution to the system of equations is x = 114/39 and y = -46/13.

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