Question

Solve the system of equations:

4x - y = -13,
y = -7x - 9.
Fill in the blanks:
x = ?
y = ?
A) x = 5, y = 32
B) x = -3, y = 16
C) x = 4, y = -5
D) x = -2, y = 5

Answer 1

The correct option is D). The solution to the system of equations 4x - y = -13 and y = -7x - 9 is found by substitution, giving x = -2 and y = 5.

Step-by-step explanation:

To solve the given system of equations, we need to find the values of x and y that satisfy both equations simultaneously. The system is:

• 4x - y = -13
• y = -7x - 9

Since the second equation gives us y in terms of x, we can substitute the expression for y from the second equation into the first equation:

4x - (-7x - 9) = -13

This simplifies to:

4x + 7x + 9 = -13

11x + 9 = -13

Subtract 9 from both sides:

11x = -22

Divide both sides by 11:

x = -2

Now plug x back into the second equation to find y:

y = -7(-2) - 9

y = 14 - 9

y = 5

Thus, the solution to the system of equations is x = -2 and y = 5.