Find the intersection point of the lines given by the equations $$ y = 2x + 1 $$ and $$ y = -0.5x + 3 $$.

Question

UpStudy AI · Accepted Answer

To find the intersection point of the two lines given by the equations:

1. $$ y = 2x + 1 $$
2. $$ y = -0.5x + 3 $$

**Step 1: Set the equations equal to each other**

Since both equations equal $$ y $$, we set them equal to find the $$ x $$-coordinate of the intersection point.

$$
2x + 1 = -0.5x + 3
$$

**Step 2: Solve for $$ x $$**

$$
2x + 0.5x = 3 - 1 \
2.5x = 2 \
x = \frac{2}{2.5} \
x = 0.8
$$

**Step 3: Substitute $$ x = 0.8 $$ into one of the original equations to find $$ y $$**

Using the first equation $$ y = 2x + 1 $$:

$$
y = 2(0.8) + 1 \
y = 1.6 + 1 \
y = 2.6
$$

**Conclusion:**

The two lines intersect at the point $$ (0.8,\ 2.6) $$.

**Alternatively, as fractions:**

$$
x = \frac{4}{5}, \quad y = \frac{13}{5}
$$

So, the intersection point is $$ \left( \frac{4}{5},\ \frac{13}{5} \right) $$.
The lines intersect at the point $$ (0.8, 2.6) $$.

Find the intersection point of the lines given by the equations \( y = 2x + 1 \) and \( y = -0.5x + 3 \).