Which of the points on the graph is a solution for the simultaneous inequalities y > 4x - 2 and y _> -1/3 x + 2?

Question

Enter the x-value followed by the y-value.
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Answer 1

To find the solution for the simultaneous inequalities, we need to find the points on the graph that satisfy both inequalities.

First, let's solve the first inequality: y > 4x - 2. To do this, we can create an equation by replacing the inequality symbol with an equals sign: y = 4x - 2.

Now, let's solve the second inequality: y ≥ -1/3x + 2. Again, we can create an equation by replacing the inequality symbol with an equals sign: y = -1/3x + 2.

Now we have two equations:

1) y = 4x - 2
2) y = -1/3x + 2

We can solve this system of equations by equating the two y-values and the two x-values.

Equating the y-values:
4x - 2 = -1/3x + 2
Multiply both sides by 3 to get rid of the fraction:
12x - 6 = -x + 6
Add x to both sides:
13x - 6 = 6
Add 6 to both sides:
13x = 12
Divide both sides by 13:
x = 12/13

Now, substitute the value of x back into one of the equations to find the y-value:
y = 4(12/13) - 2
y = 48/13 - 26/13
y = 22/13

Therefore, the solution to the simultaneous inequalities y > 4x - 2 and y ≥ -1/3x + 2 is (12/13, 22/13).