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.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the solution to both equations, we can first graph each equation and then find the point where the two lines intersect.

First, let's graph the equation 4x+3y=15:
- Rearrange the equation into slope-intercept form (y=mx+b):
3y = -4x + 15
y = (-4/3)x + 5
- Now plot the y-intercept (0,5) and use the slope to find another point. The slope is -4/3, so we move down 4 units and right 3 units from the y-intercept to find another point:
Plotting these points and drawing a line through them, we get:

Next, let's graph the equation y=x+5:
- This equation is already in slope-intercept form with a slope of 1 and a y-intercept of 5:
Plotting the y-intercept (0,5) and using the slope of 1, we get:

Now, we can see that the two lines intersect at the point (3,8). Therefore, the solution to the system of equations is x=3 and y=8.

Answer 2

wrong

Answer 3

[AI-generated answer — Bot GPT 3.5]

Let's try a different approach to find the solution to the system of equations.

Given Equations:
1) 4x + 3y = 15
2) y = x + 5

We can substitute equation 2 into equation 1 to find the values of x and y:

4x + 3(x + 5) = 15
4x + 3x + 15 = 15
7x + 15 = 15
7x = 0
x = 0

Now substitute x back into equation 2 to find y:
y = 0 + 5
y = 5

Therefore, the solution to the system of equations is x = 0 and y = 5.