#1. Because we know y is equal to 7x - 5, you can substitute 7x - 5 for y in the second equation. Then you can solve for x.
2x + y = 13
2x + (7x - 5) = 13
9x - 5 = 13
9x = 18
x = 2
Now that you know x = 2, you can solve for y.
y = 7x - 5
y = 7(2) - 5
y = 14 - 5
y = 9
To double check this, plug in 2 for x and 9 for y in the second equation.
2x + y = 13
2(2) + (9) = 13
4 + 9 = 13
13=13
Both sides equal each other so (2,9) is a solution to the system of equations.
#2. Because x = -5y - 4, you can substitute -5y - 4 for x in the second equation and solve for y.
x - 4y = 23
-5y - 4 - 4y = 23
-9y - 4 = 23
-9y = 27
y = -3
Now, plug y = -3 into y in the first equation.
x = -5(-3) - 4
x = 15 - 4
x = 11
To double check, plug in -3 for y and 11 for x in the second equation.
x - 4y = 23
11 - 4(-3) = 23
11 + 12 = 23
23 = 23
Both sides equal each other, so (11, -3) is the right solution.