Question

What is the solution for the following system of equations?

5x + 7y = 3
2x + 3y = 1
O (-1,2)
O (1,-2)
O (-2,1)
O (2,-1)

Answer 1

`(2, -1)`

Explanation:

Given the system of equations:

`\begin{cases}5x+7y=3,\\2x+3y=1\end{cases}`

Multiply the first equation by -2 and the second equation by 5, then add both equations to solve for
`y`:

`\begin{cases}-2(5x+7y)=(-2)3,\\5(2x+3y)=(5)1\end{cases},\\\begin{cases}-10x-14y=-6,\\10x+15y=5\end{cases},\\-10x+10x-14y+15y=-6+5,\\y=-1`

Substitute
`y=-1` into any equation to solve for
`x`:

`2x+3y=1,\\2x+3(-1)=1,\\2x-3=1,\\2x=4,\\x=\boxed{2}`

Therefore, the solution to this system of equations is
`\boxed{(2, -1)}`

Answer 2

Explanation:

I recommend you to use matrices for systems of equations; it's a lot faster and more expedient.