Question

What is the value of the x variable in the solution to the following system of equations?

3x − 6y = 3
7x − 5y = −11

−2

−3

x can be any number as there are infinitely many solutions to the system.

There is no x value as there is no solution to the system

Answer 1

Multiply the first equation by -5/6, add the modified equation to the second equation, and solve for x.

Answer 2

\[3x − 6y = 3 \implies -\frac{5}{2}x+5y=-\frac{5}{2}\]Add this to the second equation to get\[\frac{9}{2}x=-\frac{27}{2} \implies x=-3\]To finish the rest of the problem, we substitute back in to find y=-2, so the overall solution is\[(x,y)=(-3,-2)\]