Question

Which of the points on the graph is a solution for the simultaneous inequalities y>4x−2 and y≥−13x+2? Enter the x-value followed by the y

Answer 1

To find a solution for the simultaneous inequalities \( y > 4x - 2 \) and \( y \geq -13x + 2 \), we first can analyze the intersection points of the lines defined by the equations \( y = 4x - 2 \) and \( y = -13x + 2 \).

1. Set \( 4x - 2 = -13x + 2 \) to find the intersection:

\[
4x + 13x = 2 + 2
\]
\[
17x = 4
\]
\[
x = \frac{4}{17}
\]

2. Now plug \( x = \frac{4}{17} \) back into either equation to find \( y \). Let's use \( y = 4x - 2 \):

\[
y = 4\left(\frac{4}{17}\right) - 2
\]
\[
y = \frac{16}{17} - 2 = \frac{16}{17} - \frac{34}{17} = \frac{-18}{17}
\]

So, the intersection point is \( \left(\frac{4}{17}, \frac{-18}{17}\right) \).

3. Now we need to test a few points that satisfy both inequalities. Since we need \( y > 4x - 2 \) and \( y \geq -13x + 2 \), we can choose values for \( x \) and calculate \( y \).

For example, let's choose \( x = 1 \):

- Calculate \( y > 4(1) - 2 = 2 \) (which means \( y > 2 \)).
- Calculate \( y \geq -13(1) + 2 = -11 \) (which means \( y \geq -11 \)).

Thus, a suitable \( y \) value that satisfies both inequalities for \( x = 1 \) could be \( y = 3 \) (since \( 3 > 2 \) and \( 3 \geq -11 \)).

Therefore, a solution to the simultaneous inequalities could be \( (1, 3) \).

So, the x-value followed by the y-value is:

**1 3**