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 intersect point is (__).

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the solution to both equations, we can start by graphing them on the same coordinate system.

First, let's graph the equation 4x + 3y = 15. We can rewrite this equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

4x + 3y = 15
3y = -4x + 15
y = (-4/3)x + 5

Now, 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.

Now, we can plot the graphs of both equations on the same coordinate system.

The intersection point of the two lines is (2, 7).

Therefore, the solution to both equations is x = 2 and y = 7.

Answer 2

wrong

Answer 3

[AI-generated answer — Bot GPT 3.5]

I apologize for the error. Let's try again to find the correct solution.

Given the system of equations:
1) 4x + 3y = 15
2) y = x + 5

We can substitute equation (2) into equation (1) to solve for x:
4x + 3(x + 5) = 15
4x + 3x + 15 = 15
7x + 15 = 15
7x = 0
x = 0

Now, substitute x = 0 back into equation (2) to solve for y:
y = 0 + 5
y = 5

Therefore, the solution to the system of equations is x = 0 and y = 5. The intersection point is (0, 5).

Answer 4

Review the graphs of a system of two linear equations in two variables: y = x - 6 and y = -x + 4. Find the solution to both equations. The intersect point is (__).

Answer 5

[AI-generated answer — Bot GPT 3.5]

To find the solution to both equations, we can write the system as:

1) y = x - 6
2) y = -x + 4

To find the intersect point, we set the two equations equal to each other:

x - 6 = -x + 4
2x = 10
x = 5

Now, we substitute x = 5 into either equation to find y:

y = 5 - 6
y = -1

Therefore, the solution to the system of equations is x = 5 and y = -1. The intersect point is (5, -1).

Answer 6

Estimate the intersection point of the graphs of the following linear equations in two variables.

y = x + 2
y = -x + 6

Answer 7

[AI-generated answer — Bot GPT 3.5]

To find the intersection point of the graphs of the given linear equations, we will solve the system of equations:

1) y = x + 2
2) y = -x + 6

Since both equations are already in the form y = mx + b (slope-intercept form), we can compare the slope and y-intercept to determine the intersection point.

The first equation has a slope of 1 (coefficient of x) and a y-intercept of 2.
The second equation has a slope of -1 (coefficient of x) and a y-intercept of 6.

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

x + 2 = -x + 6
2x = 4
x = 2

Now, substitute x = 2 into either equation to find y:

y = 2 + 2
y = 4

Therefore, the intersection point of the graphs of the two equations y = x + 2 and y = -x + 6 is (2, 4).

Answer 8

Estimate the intersection point of the graphs of the following linear equations in two variables.

y = -x + 7
y = 4x - 3

Answer 9

[AI-generated answer — Bot GPT 3.5]

To find the intersection point of the graphs of the given linear equations, we will solve the system of equations:

1) y = -x + 7
2) y = 4x - 3

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

-x + 7 = 4x - 3
5x = 10
x = 2

Now, substitute x = 2 into either equation to find y:

y = -2 + 7
y = 5

Therefore, the intersection point of the graphs of the two equations y = -x + 7 and y = 4x - 3 is (2, 5).