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

Question

6x-2y=6
2x+3y=2

Answer 1

To solve the simultaneous linear equations, we can first rearrange the equations to solve for y:

Equation 1: 6x - 2y = 6
-2y = -6x + 6
y = 3x - 3

Equation 2: 2x + 3y = 2
3y = -2x + 2
y = (-2/3)x + 2/3

Now that we have both equations in the form y = mx + b, we can set them equal to each other to find the intersection point:

3x - 3 = (-2/3)x + 2/3
Multiplying by 3 to clear the denominator:
9x - 9 = -2x + 2
Adding 2x and 9 to both sides:
11x = 11
x = 1

Now we can plug x = 1 back into either equation to solve for y:

y = 3(1) - 3
y = 0

Therefore, the solutions to the simultaneous equations are x = 1 and y = 0.

To draw the graph and show the intersection point of the two lines, plot the points (1,0):

Graph:
The first line (6x - 2y = 6) will go through the points (0,-3) and (2,0).
The second line (2x + 3y = 2) will go through the points (0,2/3) and (1,0).
The intersection point is at (1,0) where both lines cross on the graph.

Answer 2

How do I plot 2/3 into the graph, please explain?

Answer 3

To plot 2/3 on the graph:

Since 2/3 is a fraction, you can convert it to a decimal to make it easier to plot. The decimal equivalent of 2/3 is approximately 0.67.

Now, when you plot the point (0, 0.67) on the graph, this represents the y-coordinate of the second line (2x + 3y = 2) when x = 0.

To plot the point on the graph:
1. Find the point where the y-axis intersects the line (0, 0.67).
2. Go along the x-axis to where x = 0.
3. Go up the y-axis to where y = 0.67.
4. Mark this point on the graph.

By following these steps, you can accurately plot the point representing 2/3 (or 0.67) on the graph.