Question

Solve each of these systems of equations. You may use either the substitution or elimination method.2x+y=15x+6y =4

Answer 1

x=2/7 and y=3/7

Step-by-step explanation:

Given the systems of equations:

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

We use the substitution method to solve.

Step 1: Make y the subject in the first equation.

`\begin{gathered} 2x+y=1 \\ y=1-2x \end{gathered}`

Step 2: Substitute y into the second equation.

`\begin{gathered} 5x+6y=4 \\ 5x+6(1-2x)=4 \\ 5x+6-12x=4 \\ 5x-12x=4-6 \\ -7x=-2 \\ x=-(2)/(-7) \\ x=(2)/(7) \end{gathered}`

Step 3: Solve for y

`\begin{gathered} y=1-2x \\ =1-2((2)/(7)) \\ =1-(4)/(7) \\ y=(3)/(7) \end{gathered}`

Therefore, x=2/7 and y=3/7.