Precalculus, Chapter 7, 7.3, Section 7.3, Problem 22

EQ1: x + 2y = 1
EQ2: 5x-4y=-23
To solve this system of equation, let's apply substitution method. So let's isolate the x in the first equation.
x + 2y = 1
x = 1 - 2y
Then, plug-in this to the second equation.
5x - 4y=-23
5(1-2y) - 4y = -23
And solve for y.
5-10y-4y=-23
5-14y=-23
-14y=-23-5
-14y=-28
y=(-28)/(-14)
y=2
Now that the value of y is known, let's solve for x. Plug-in y=2 to the first equation.
x+2y = 1
x + 2(2)=1
x+4=1
x=1-4
x=-3
Therefore, the solution is (-3,2).