Question

Solve the simultaneous linear equations and find the solutions x and y. Draw the graph to show the intersection point of the two lines?

Answer 1

[AI-generated answer — Bot GPT 3.5]

Let's start with the simultaneous linear equations:

1) 2x + 3y = 11
2) 5x - y = 3

To solve these equations, we can use the method of substitution or elimination.

Let's first use the elimination method to solve these equations:

Multiply equation 2 by 3:
3(5x - y) = 3(3)
15x - 3y = 9

Now we have:
2x + 3y = 11
15x - 3y = 9

Add the two equations together:
17x = 20
x = 20 / 17
x = 1.176

Now substitute x back into equation 1:
2(1.176) + 3y = 11
2.353 + 3y = 11
3y = 8.647
y = 8.647 / 3
y = 2.882

So, the solution to the simultaneous linear equations is:
x = 1.176
y = 2.882

Now, let's draw the graph of these two equations to show the intersection point.

The graph of equation 1: 2x + 3y = 11 can be rewritten as y = (-2/3)x + 11/3
And the graph of equation 2: 5x - y = 3 can be rewritten as y = 5x - 3

Now we can plot both equations on a graph and find the intersection point:

The intersection point is at the coordinates (1.176, 2.882).

I hope this helps! Let me know if you need any further assistance.

Answer 2

Solve the simultaneous linear equations and find the solutions x and y. Draw the graph and show the intersection point of the two lines.

4x+y=12
3x-y=2

Answer 3

[AI-generated answer — Bot GPT 3.5]

To solve the simultaneous linear equations 4x + y = 12 and 3x - y = 2, we can use the elimination method.

1) 4x + y = 12
2) 3x - y = 2

Add equations 1 and 2 together:
(4x + y) + (3x - y) = 12 + 2
7x = 14
x = 14 / 7
x = 2

Substitute x = 2 back into equation 1:
4(2) + y = 12
8 + y = 12
y = 12 - 8
y = 4

So, the solution to the simultaneous linear equations is:
x = 2
y = 4

Now let's draw the graph of the two equations to show the intersection point:

Equation 1: 4x + y = 12
y = -4x + 12

Equation 2: 3x - y = 2
y = 3x - 2

Now we can plot both equations on a graph:

The intersection point of the two lines is at the coordinates (2, 4).

I hope this helps! Let me know if you need any further assistance.

Answer 4

Could you clarify why and how did you write the equations again in a different way like, you changed 4x+y=12 to y=-4x +12 and the equation 3x-y =2 to y=3x-2 , please explain why and how?

Answer 5

[AI-generated answer — Bot GPT 3.5]

I apologize for the confusion. Let's clarify how we rewrote the equations in the form y = mx + b:

Given equations:

1) 4x + y = 12
2) 3x - y = 2

To rewrite these equations in slope-intercept form (y = mx + b), we isolate y on one side of the equation:

1) 4x + y = 12
Subtract 4x from both sides:
y = -4x + 12

2) 3x - y = 2
Add y to both sides and then add 2:
y = 3x - 2

This will help us easily graph the lines by identifying the slope (m) and y-intercept (b) of the equations. The slope (m) represents the rate of change of y with respect to x, and the y-intercept (b) is the value of y when x = 0.

By rewriting the equations in slope-intercept form, we can easily identify the slope and y-intercept for each line and graph them accurately to find the intersection point, which in this case, is the solution to the simultaneous equations.

I hope this explanation clarifies why and how we rewrote the equations in a different form. Let me know if you need further clarification.

Answer 6

So what will be the actual numbers to plot on the graph,is it the solutions to the equations which are 2 and 4 or which?

Answer 7

[AI-generated answer — Bot GPT 3.5]

Apologies for the oversight. The actual numbers to plot on the graph are the solutions to the simultaneous equations, which are x = 2 and y = 4. These solutions represent the coordinates of the intersection point of the two lines.

To plot the lines on the graph:
1. Equation 1: 4x + y = 12
Rewrite as y = -4x + 12
With x = 0, y = 12 -> First point (0, 12)
With x = 3, y = 0 -> Second point (3, 0)
Draw this line on the graph.

2. Equation 2: 3x - y = 2
Rewrite as y = 3x - 2
With x = 0, y = -2 -> First point (0, -2)
With x = 2, y = 4 -> Second point (2, 4)
Draw this line on the graph.

The intersection point of the two lines will be at the coordinates (2, 4), which is represented by the solutions to the equations.

I hope this clarifies the numbers to plot on the graph. Let me know if you have any more questions.