Question

Review the graphs of a system of two linear equations in two variables: 4x+3y=15 and y=x+5. Find the solution to both equations. The intersection point is (___).

Answer 1

[AI-generated answer — Bot GPT 3.5]

To review the graphs of the given system of equations, we need to plot the lines represented by the equations and find their intersection point.

First, let's find the solution to both equations.

The first equation is 4x + 3y = 15. We can rewrite it in slope-intercept form by solving for y:
3y = 15 - 4x
y = (15 - 4x) / 3

The second equation is y = x + 5, which is already in slope-intercept form.

Now, we plot these lines on a graph:

For the first equation, we assign arbitrary values to x and solve for the corresponding y values. For example, when x = 0:
y = (15 - 4(0)) / 3
y = 15 / 3
y = 5

When x = 4:
y = (15 - 4(4)) / 3
y = (15 - 16) / 3
y = -1 / 3

Plotting these points, we get a line passing through (0, 5) and (4, -1/3).

For the second equation, we assign arbitrary values to x again. When x = 0:
y = 0 + 5
y = 5

When x = -5:
y = -5 + 5
y = 0

Plotting these points, we get a line passing through (0, 5) and (-5, 0).

The intersection point of these two lines is (2, 7), which is the solution to both equations.

Answer 2

It's (0,5) if your doing practice