Which of the points on the graph is a solution for the simultaneous inequalities y>4x−2

Question

and y≥−13x+2?
Enter the x-value followed by the y-valu

Answer 1

To find a solution for the simultaneous inequalities \( y > 4x - 2 \) and \( y \geq -13x + 2 \), we need to identify points that satisfy both inequalities.

1. Plot the boundaries of the inequalities:

   • The boundary for \( y = 4x - 2 \) is a line where the region above this line (not including the line itself) is valid for the first inequality.
   • The boundary for \( y = -13x + 2 \) is a line where the region above this line (including the line) is valid for the second inequality.

2. Find an intersection point or a point in the valid region:

   • Let's check the point \( (1, 3) \):
     • For \( y > 4x - 2 \): \[ 3 > 4(1) - 2 \implies 3 > 2 \quad \text{(True)} \]
     • For \( y \geq -13x + 2 \): \[ 3 \geq -13(1) + 2 \implies 3 \geq -13 + 2 \implies 3 \geq -11 \quad \text{(True)} \] Therefore, the point \( (1, 3) \) satisfies both inequalities.

As a result, a solution for the simultaneous inequalities is \( 1, 3 \).