Answer:
Solutions: x = 7, y = 9; or (7, 9)
Step-by-step explanation:
Given the following systems of linear equations:
7x - 8y = -23
7x - 7y = -14
Since the coefficients of x in the given system have the same sign, we could use the process of elimination by subtracting the two equations.
7x - 8y = -23
- 7x - 7y = -14
-y = -9
Divide both sides by -1 to solve for y:
[tex]\frac{-y}{-1} = \frac{-9}{-1}[/tex]
y = 9
Substitute the value of y into either one of the given equations to solve for x:
7x - 7y = -14
7x - 7(9) = -14
7x - 63 = -14
Add 63 to both sides:
7x - 63 + 63 = -14 + 63
7x = 49
Divide both sides by 7 to solve for x:
[tex]\frac{7x}{7} = \frac{49}{7}[/tex]
x = 7
Double-check whether x = 7 and y = 9 are valid solutions to the given system:
x = 7, y = 9:
7(7) - 8(9) = -23
49 - 72 = -23
-23 = -23 (True statement).
7(7) - 7(9) = -14
49 - 63 = -14
-14 = -14 (True statement).
Therefore, the solution to the given systems of linear equations are x = 7, and y = 9, or (7, 9).
