COULD SOME OF WITH DEGREE IN MATHS HELP ME TO SOLVE THIS SIMULTANEOUS EQUATION PLEASE, PLEASE ?
I HAVE RIED DIFFERENT METHODS BUT IT CANNOT GET THE CORRECT ANSWER, AS IN THE BOOK.
X-3/4 -Y-2/5 = -1/4 (1)
4-X/3+ 3-Y/2 = - 13/20 (2)
5x-15-4y+8= -1
5x-4y=17-1
8-2x+9-3y= -13
-2x-3y= 17-13
-2x -3y= 4
10x-8y= 32
-6x-9y = 4
4x+y= 12
thank
mohammad from uk london
Hard to tell, but it appears that you have
(x-3)/4 - (y-2)/5 = -1/4
(4-x)/3 + (3-y)/2 = -13/20
which is the same as
5x - 4y = 2
20x + 30y = 209
20x-16y = 8
20x+30y = 209
46y = 201
so,
x = 448/115
y = 201/46
Hmmm. Maybe you had
x - 3/4 - y - 2/5 = -1/4
4 - x/3 + 3 - y/2 = -13/20
Clearing fractions, we have
10x-10y = 9
20x+30y = 459
x = 243/25
y = 441/50
Sure, I can help you solve this simultaneous equation. Let's start by writing down the equations that you've provided:
Equation (1): x - (3/4) - y - (2/5) = -1/4
Equation (2): 4 - x/3 + 3 - y/2 = -13/20
To solve these equations, we can use the method of substitution or the method of elimination. I'll demonstrate both methods for you.
Method 1: Substitution
Step 1: In Equation (1), let's solve for x in terms of y.
x - (3/4) - y - (2/5) = -1/4
x = y + (1/4) - (2/5) - (1/4)
x = y - (2/5)
Step 2: Substitute this expression for x in Equation (2).
4 - (y - 2/5)/3 + 3 - y/2 = -13/20
Step 3: Simplify and solve the resulting equation for y.
Multiply both sides of the equation by 60 (common denominator) to eliminate the fractions:
60(4) - 20(y - 2/5) + 60(3) - 30y = 60(-13/20)
240 - 4(y - 2/5) + 180 - 30y = -39
240 - 4y + 8/5 + 180 - 30y = -39
Combine like terms:
420 - 34y + 8/5 = -39
Multiply both sides by 5 to eliminate the fraction:
2100 - 170y + 8 = -195
Combine like terms:
2108 - 170y = -195
Rearrange the equation and solve for y:
-170y = -195 - 2108
-170y = -2303
y = -2303 / -170
y ≈ 13.5529
Step 4: Substitute the value of y back into Equation (1) to solve for x.
x - (3/4) - (13.5529) - (2/5) = -1/4
Multiply both sides by 20 (common denominator) to eliminate the fractions:
20x - 15 - 271.058 - 8 = -5
Combine like terms:
20x - 294.058 - 23 = -5
20x - 317.058 = -5
Add 317.058 to both sides of the equation:
20x = 312.058
Divide both sides by 20 to solve for x:
x = 312.058 / 20
x ≈ 15.6029
So the solution to this simultaneous equation is approximately x ≈ 15.6029 and y ≈ 13.5529.
Now let's check if these values satisfy both equations (1) and (2).