Question

Solve the following simultaneous equation using any suitable method 4x+3y=18,3x-4y=11.5​ a) Substitution method

b) Elimination method
c) Graphical method
d) Matrix method

Answer 1

The solution to the simultaneous equations 4x+3y=18 and 3x-4y=11.5 using the elimination method is x=4.4 and y=0.32 after aligning coefficients and subtracting the second equation from the first.

Step-by-step explanation:

To solve the simultaneous equations 4x+3y=18 and 3x-4y=11.5, we can use the elimination method. First, we multiply the first equation by 3 and the second equation by 4 to align the coefficients of x:

• 3*(4x+3y) = 3*18
• 4*(3x-4y) = 4*11.5

Which gives us:

• 12x + 9y = 54
• 12x - 16y = 46

Subtracting the second equation from the first gives us:

25y = 8

Dividing both sides by 25, we get:

y = 8 / 25

Now we can plug the value of y into the first equation:

4x + 3*(8/25) = 18

Multiplying out the brackets and rearranging, we can solve for x:

x = (18 - 3*(8/25)) / 4

After calculating, we find that x = 4.4 and y = 0.32, which is the solution to the system of equations.