Question

Estimate the solution to the system of these linear equations based on the graph.

y=2x+3
y=1/2x+6

(1 point)
Responses

(2,7)

(2,−7)

(7,2)

(−2,7 )

Answer 1

To estimate the solution to the system of linear equations based on the provided equations, we'll first find the point where the lines intersect by calculating the point of intersection algebraically.

The equations are:

1. \( y = 2x + 3 \)
2. \( y = \frac{1}{2}x + 6 \)

To find the intersection, set the two equations equal to each other:

\[ 2x + 3 = \frac{1}{2}x + 6 \]

Now, get rid of the fraction by multiplying the entire equation by 2:

\[ 4x + 6 = x + 12 \]

Now, isolate \( x \):

\[ 4x - x = 12 - 6 \]
\[ 3x = 6 \]
\[ x = 2 \]

Now that we have \( x \), we can substitute it back into either of the original equations to find \( y \). Using the first equation:

\[ y = 2(2) + 3 \]
\[ y = 4 + 3 \]
\[ y = 7 \]

Thus, the point of intersection is \( (2, 7) \).

So the solution to the system of equations is:

**(2, 7)**.