Question

Which of the following approaches result in an equation in one variable? Select all that apply

$3x+y=7$ Equation 1


$-x-2y=16$ Equation 2



Responses



Add the equations.

Add the equations.



Multiply Equation 2 by 3 and subtract the equations.

Multiply Equation 2 by 3 and subtract the equations.



Multiply Equation 1 by 2 and add the equations.

Multiply Equation 1 by 2 and add the equations.



Solve Equation 1 for y and substitute the result in Equation 2

Answer 1

The solution to the system of equations is x=6 and y=−11. This is an equation in one variable (each variable is isolated).

To get an equation in one variable, you can use various methods like substitution or elimination to eliminate one of the variables. Let's examine these equations:

Equation 1:

3x+y=7

Equation 2:

−x−2y=16

We can use the substitution method or elimination method to obtain an equation in one variable.

By rearranging Equation 1 to make y the subject:

y=7−3x

Now we substitute this expression for y into Equation 2:

−x−2(7−3x)=16

This simplifies to:

−x−14+6x=16

Combining like terms:

5x−14=16

Adding 14 to both sides:

5x=30

Dividing by 5:

x=6

Now that we have found x=6, we can substitute it into either Equation 1 or Equation 2 to solve for y.

Using Equation 1:

3x+y=7

3(6)+y=7

18+y=7

y=7−18

y=−11

Therefore, the solution to the system of equations is x=6 and y=−11. This is an equation in one variable (each variable is isolated).