Question

Solve this system of equations without graphing and show yourreasoning:5x + y = 720x + 2 = y

Answer 1

We can use substitution method to solve this equation.

Given

5x + y = 7 ---------------------------------------------------------- Equation 1

20x + 2 = y ---------------------------------------------------------- Equation 2

We can substitute Equation 2 into Equation 1, thus, we have:

`\begin{gathered} 5x+y=7 \\ 5x+(20x+2)=7 \\ 5x+20x+2=7 \end{gathered}`

Now, we have an equation in x. We can do algebra and solve for x. Shown below:

`\begin{gathered} 5x+20x+2=7 \\ 25x=5 \\ x=(5)/(25) \\ x=(1)/(5) \end{gathered}`

Now, we use this value of x and substitute into equation 2 to find the value of y. Shown below:

`\begin{gathered} y=20x+2 \\ y=20((1)/(5))+2 \\ y=4+2 \\ y=6 \end{gathered}`

Final solution:

`x=(1)/(5),y=6`