Question

Solve the system of linear equations by substitution. 8x−1/3y=0; 12x+3=y

Please help!

Answer 1

To solve the system of linear equations by substitution, solve one equation for one variable and then substitute that expression into the other equation. In this case, solve equation (2) for y and substitute it into equation (1) to find the values of x and y.

Step-by-step explanation:

To solve the system of linear equations by substitution, we will solve one equation for one variable and then substitute that expression into the other equation. Let's solve the system:

8x - ⅓y = 0 ...(1)

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

From equation (2), we can express y in terms of x: y = 12x + 3. Now substitute this expression for y in equation (1):

8x - ⅓(12x + 3) = 0

Simplify the equation and solve for x:

8x - 4x - 1 = 0

4x - 1 = 0

4x = 1

x = ⅓

Substitute this value of x back into equation (2) to find y:

y = 12(⅓) + 3

y = 9

So, the solution to the system of linear equations is x = ⅓ and y = 9.

Answer 2

Substitution involves replacing part of one equation with the other equation. In this case, the second equation is already solved for y. All we have to do is replace y in the first equation with 12x+3.

8x - (1/3)(12x+3) = 0

Distribute the -1/3

8x - 4x - 1 = 0

4x - 1 = 0

4x = 1

x = 1/4

Now plug 1/4 in for x to solve for y.

12(1/4) + 3 = y

y = 6

Answer: (1/4, 6)