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:

First, we can rewrite the two equations in slope-intercept form:
6x - 2y = 6
-2y = -6x + 6
y = 3x - 3

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

Now we have the two equations in slope-intercept form:
y = 3x - 3
y = (-2/3)x + 2/3

To find the intersection point, we can set the two equations equal to each other and solve for x:
3x - 3 = (-2/3)x + 2/3
3x + (2/3)x = 2 + 3
(11/3)x = 5
x = 15/11

Now that we have found x, we can substitute it back into one of the equations to find y:
y = 3(15/11) - 3
y = 45/11 - 3
y = 6/11

So, the solution to the simultaneous linear equations is x = 15/11 and y = 6/11.

To draw the graph and show the intersection point:
Graph the two lines y = 3x - 3 and y = (-2/3)x + 2/3 on the same coordinate plane. The intersection point of the two lines should be at (15/11, 6/11).