Answer
$\{(4,-2)\}$
Work Step by Step
We are given the system of equations as:
$$5x+7y=6 \quad\quad \quad(1) \\ 10x-3y=46 \quad \quad(2)$$
By multiplying $-2$ to the first equation. we get an equivalent equation:
$$-10x-14y=-12 \quad \quad(3)$$
Add equations $(2)$ and $(3)$ to eliminate $x$ and then solve for $y$.
$$-17y=34 \implies y=-2$$
Plug $y=2$ into the first equation then solve for x to obtain:
$$5x+7(-2)=6 \\ 5x-14=6 \\x=4$$
So, the solution set is $\{(4,-2)\}$.
