Question

How do solve the following linear system?: `-3x + 7y= -16 , -9x + 5y = 16`?

Answer 1

I really like to use the substitution method for solving linear systems.

Explanation:

So how that works is we start by putting the two equations into y-intercept form. So that means that our first equation becomes
y=(3/7)x-(16/7) and the second equation becomes y=(9/5)x+(16/5)

From there, you can choose either equation and plug that value into the other equation. Let's say I choose the first equation to be plugged into the second equation. I take the value of y from the first equation and substitute that in for y in the second equation, so the equation we're left with is:
(3/7)x-(16/7)=(9/5)x+(16/5)

We can use basic algebraic skills to solve for x, leaving us with this value for x:
x=(-4)

We plug that value back into either equation, which allows us to solve for y. Both equations give us the following equation for y:
y=(-4)

So the solution for this system of equations is (-4,-4), which basically means that if you plotted the two equations that we started with on a graph, the solution would be the intersection of the two lines.