Question

What is the x-value of the solution to the system of equations shown below? 2x + y = 20 6x - 5y = 12

Answer 1

Given the equation system:

`\begin{gathered} 1)2x+y=20 \\ 2)6x-5y=12 \end{gathered}`

To solve the system and determine the value of x, first step is to write one of the equations in terms of y:

`\begin{gathered} 2x+y=20 \\ y=20-2x \end{gathered}`

Then replace this expression in the second equation

`\begin{gathered} 6x-5y=12 \\ 6x-5(20-2x)=12 \end{gathered}`

Now that you have an expression with only one unknown, x, you can calculate its value.

Solve the parenthesis using the distributive property of multiplication

`\begin{gathered} 6x-5\cdot20-5\cdot(-2x)=12 \\ 6x-100+10x=12 \\ 6x+10x-100=12 \\ 16x=12+100 \\ 16x=112 \\ (16x)/(16)=(112)/(16) \\ x=7 \end{gathered}`