Answer :
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To find the value of k for which the system of equations has infinitely many solutions, we need to set the equations equal to each other and solve for x. Let's start by solving the given equation:
-3x + 1 = 1/4
To make the calculations easier, we can multiply both sides of the equation by 4 to get rid of the fraction:
-3x + 1 = 1/4
4*(-3x + 1) = 4*(1/4)
-12x + 4 = 1
Now, we isolate x by moving the constants to one side:
-12x = 1 - 4
-12x = -3
Divide by -12 to solve for x:
x = -3 / -12
x = 1/4
Now that we have found the value of x, let's substitute it back into the equation with k to see for what value of k the system has infinitely many solutions:
-3(1/4) + 1 = k
-3/4 + 1 = k
-3/4 + 4/4 = k
1/4 = k
Therefore, for k = 1/4, the system of equations will have infinitely many solutions.
