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 $y\ge -13x+2$, 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 $(\frac{4}{17},\frac{-18}{17})$.

3. Now we need to test a few points that satisfy both inequalities. Since we need $y>4x-2$ and $y\ge -13x+2$, 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 $y\ge -13(1)+2=-11$ (which means $y\ge -11$).

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

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

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

1 3