Question

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How many solutions does the system of equations have? y = -2x + 12 4y + x 200 (1 point) One solution Two solutions No solution O Infinitely many solutions

Answer 1

To determine the number of solutions, we need to solve the system of equations:

1) y = -2x + 12
2) 4y + x = 200

We can solve these equations by substituting the value of y from equation 1 into equation 2:

4(-2x + 12) + x = 200
-8x + 48 + x = 200
-7x + 48 = 200
-7x = 152
x = -152/7 ≈ -21.71

Substituting this value of x back into equation 1 gives us:

y = -2(-21.71) + 12
y = 43.42 + 12
y = 55.42

Therefore, the system of equations has exactly one solution.