Question

Solve the system using elimination.2x+10y=83x-10y=12

Answer 1

x=4, y=0

Step-by-step explanation

Step 1

Let

`\begin{gathered} 2x+10y=8\text{ Equation (1)} \\ 3x-10y=12\text{ Equation (2)} \end{gathered}`

Step 2

add equation (1) and equation(2) to eliminate y

`\begin{gathered} 2x+10y=8\text{ } \\ 3x-10y=12\text{ } \\ ---------- \\ 5x+0=20 \\ 5x=20 \\ \text{divide both sides by 5} \\ (5x)/(5)=(20)/(5) \\ x=4 \end{gathered}`

Step 3

now, let's find y:

replace the value of x in equation (1) and isolate y

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

now, isolate y

`\begin{gathered} 8+10y=8 \\ \text{subtract 8 in both sides} \\ 8+10y-8=8-8 \\ 10y=0 \\ \text{Divide both sides by 10} \\ (10y)/(10)=(0)/(10) \\ y=0 \end{gathered}`

so, the answer is

`x=4,\text{ y=0}`

we can verify

`\begin{gathered} 2x+10y=8\text{ Equation (1)} \\ 2(4)+10(0)=8\text{ } \\ 8+0=8 \\ 8=8\text{ true} \\ \text{and} \\ 3x-10y=12\text{ Equation (2)} \\ 3(4)-10(0)=12\text{ } \\ 12-0=12 \\ 12=12\text{ true} \end{gathered}`

I hope this helps you