Question

Solve this system using ANY method. 3x + 6y = 04x = 2y-10

Answer 1

To solve this question, let's choose the substitution method. So, you can follow the steps to find x and y.

Step 1: Isolate x in the first equation.

To isolate x:

First, subtract 6y from each side of the equation.

Second, divide both sides by 3.

`\begin{gathered} 3x+6y=0 \\ 3x+6y-6y=0-6y \\ 3x=-6y \\ (3x)/(3)=(-6y)/(3) \\ x=-2y \end{gathered}`

Step 2: Substitute x by -2y in the second equation.

`\begin{gathered} 4x=2y-10 \\ 4\cdot(-2y)=2y-10 \\ -8y=2y-10 \end{gathered}`

Step 3: Isolate y in the equation found in step 2.

To isolate y:

First, subtract 2y from both sides of the equation.

Second, divide both sides by -10.

`\begin{gathered} -8y=2y-10 \\ -8y-2y=2y-10-2y \\ -10y=-10 \\ (-10y)/(-10)=(-10)/(-10) \\ y=1 \end{gathered}`

Step 4: Find x by using the relation found in step 1.

Use the equation found in step 1 and substitute y by 1.

`\begin{gathered} x=-2y \\ x=-2\cdot(1) \\ x=-2 \end{gathered}`

Answer:

x = -2 and y = 1

or

(-2, 1)