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:

$\begin{gathered} \frac{11y}{11}=\frac{11}{11} \\ y=\frac{11}{11} \\ y=1 \end{gathered}$

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:

$\begin{gathered} \frac{-16}{4}=\frac{4x}{4} \\ -4=x \end{gathered}$

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)