Estimate the solution to the solution to the system of these linear equations based on the graph: y=2x+3 and y=1 over 2x+6

Answer 1

To estimate the solution to the system of equations based on the graph, we need to identify the point where the two lines intersect.

The two equations are:
1) y = 2x + 3
2) y = 1 / (2x + 6)

To find the intersection point, we need to set the two equations equal to each other:
2x + 3 = 1 / (2x + 6)

To simplify the equation, let's find a common denominator by multiplying both sides by (2x + 6):
(2x + 3)(2x + 6) = 1

Expanding the left side of the equation:
4x² + 18x + 18 = 1

Rearranging the equation:
4x² + 18x + 17 = 0

Using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a)

Calculating the values of the quadratic formula, we find two possible values for x: x ≈ -1.5 and x ≈ -3.25.

Now, we can substitute these values of x back into one of the original equations to find the corresponding y-values.

For x ≈ -1.5, using the equation y = 2x + 3:
y ≈ 2(-1.5) + 3
y ≈ -3 + 3
y ≈ 0

For x ≈ -3.25, using the equation y = 2x + 3:
y ≈ 2(-3.25) + 3
y ≈ -6.5 + 3
y ≈ -3.5

So, based on the graph, the estimated solution to the system of equations is approximately (-1.5, 0) and (-3.25, -3.5).