Question

Explain the system of equations 36x-8y^2x=3 and y=-6.

Answer 1

The solution to the system of equations
`36x - 8y^2x` = 3 and y = -6 is x = -1/2 and y = -6.

Step-by-step explanation:

To solve this system of equations, we'll substitute the value of y from the second equation into the first equation. Start by replacing y with -6 in the first equation:

`\[36x - 8(-6)^2x = 3.\]`

Simplify the equation step by step. First, calculate -6 squared:

`\[36x - 8(36)x = 3.\]`

Now, perform the multiplication:

`\[36x - 288x = 3.\]`

Combine like terms:

`\[-252x = 3.\]`

Divide by -252 to solve for x:

`\[x = (-1)/(2).\]`

Now that we have the value for x, substitute it back into the second equation to find y:

`\[y = -6.\]`

So, the solution to the system is x = -1/2 and y = -6. This means that when x is equal to -1/2 and y is equal to -6, both equations are satisfied simultaneously. This process of substitution and solving step by step helps us find the values that satisfy both equations in the system.