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

Step-by-step explanation:

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

Answer 2

Answer:

$(2, -1)$

Step-by-step 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 $\boxed{(2, -1)}$