Question

Solve the following system of equations. -16y = 4x 4x + 27y = 11 Enter the solution as an ordered pair:(

Answer 1

The system of equations we have is:

`\begin{gathered} -16y=4x \\ 4x+27y=11 \end{gathered}`

Step 1. Substitute the first equation into the second equation.

We substitute the value of 4x by the value of -16y:

`-16y+27y=11`

Step 2. Solve the previous equation for y.

We add the like terms in the left side of the equation:

`11y=11`

Step 3. Divide both sides of the equation by 11:

`\begin{gathered} (11y)/(11)=(11)/(11) \\ y=(11)/(11) \\ y=1 \end{gathered}`

Step 4. Now that we know that y=1, we substitute this value into the first equation of the system of equations:

`-16y=4x`

since y=1, we get:

`\begin{gathered} -16(1)=4x \\ -16=4x \end{gathered}`

Step 5. Divide both sides of the equation by 4:

`\begin{gathered} (-16)/(4)=(4x)/(4) \\ -4=x \end{gathered}`

Step 6. Write the solution as an ordered pair.

We remember than an ordered pair has the general form:

`(x,y)`

The first number is always the x value, and the second number is always the y value.

Since in this case, we have:

x=-4

and

y=1

The ordered pair will be:

`(-4,1)`

Answer: (-4,1)