Question

Estimate the intersection point of the graphs of the following linear equations in two variables.
y=x+2y=x+2

y=−x+6y=−x+6 Estimate the intersection point of the graphs of the following linear equations in two variables.
y=x+2y=x+2

y=−x+6y=−x+6

(1 point)
()
Check answer

(1 point)
()
Check answer

Answer 1

To find the intersection point of the two linear equations given, we will set the two equations equal to each other and solve for \( x \) and then for \( y \).

The equations are:
1. \( y = x + 2 \)
2. \( y = -x + 6 \)

Setting the two equations equal to each other:
\[
x + 2 = -x + 6
\]

Now, solve for \( x \):
1. Add \( x \) to both sides:
\[
x + x + 2 = 6
\]
2. Combine like terms:
\[
2x + 2 = 6
\]
3. Subtract 2 from both sides:
\[
2x = 4
\]
4. Divide by 2:
\[
x = 2
\]

Now that we have \( x \), substitute it back into one of the original equations to find \( y \). We'll use the first equation:
\[
y = x + 2
\]
Substituting \( x = 2 \):
\[
y = 2 + 2 = 4
\]

Therefore, the intersection point is \( (2, 4) \).

So, the answer is:
**Intersection point: (2, 4)**