Question

Mathematics verified5x + 7y = 93x + 7y = 11

Answer 1

We have to solve this system of linear equations.

As we have the same coefficient for y, the most effective method to solve this is by elimination: we substract the first equation from the second one and then solve for x, as y is no longer part of this new equation.

We then substract the equations:

`\begin{gathered} (3x+7y)-(5x+7y)=11-9 \\ 3x-5x+7y-7y=2 \\ -2x+0y=2 \\ -2x=2 \end{gathered}`

Then, we can solve for x:

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

Then, we can pick any of the two equations and, with the value of x = -1, we can solve for y as:

`\begin{gathered} 5x+7y=9 \\ 5(-1)+7y=9 \\ -5+7y=9 \\ 7y=9+5 \\ 7y=14 \\ y=(14)/(7) \\ y=2 \end{gathered}`

Answer: x = -1 and y = 2.