Question

Choose the ordered pair that is a solution to the system of equations.

3x + 5y = 1
x + 4y = 5

Answer 1

This can be solved in two ways: through elimination or substitution.
With this problem, it'll be easier to solve through substitution.

3x+5y=1
x+4y=5

First, look at the 2nd equation (x+4y=5) and solve for x. You'll get
x=-4y+5.
Then plug in/substitute -4y+5 into the position of x in the 1st equation (3x+5y=1).
Once you're done substituting, you'll get 3(-4y+5)+5y=1. Then just solve for y.
3(-4y+5)+5y=1
-12y+15+5y=1
-7y+15=1
-7y=-14
y=2

Now that you have the value of Y, you can substitute that value into one of the equations and get your value for x. I'll use the 2nd equation, but it doesn't matter which one you choose. You'll still get the same answer.

x+4y=5
x+4(2)=5
x+8=5
x=-3

So now that we've solved for both x and y, we can write it in the form of a coordinate/ordered pair.
x=-3 & y=2
(x,y) --> (-3,2).