How do I solve this simultaneous equation
3x-2y=5 (1)
2y-5x=9 (2)
I managed to find the value of x and that is -7 but I am having problems to substitute it's value in equation (1)
sums phonics suptracting
To solve a simultaneous equation like this, you need to use a method called substitution. Let's go step by step:
Step 1: Solve one equation for one variable in terms of the other variable. In this case, let's solve equation (1) for x in terms of y:
3x - 2y = 5
3x = 5 + 2y
x = (5 + 2y) / 3
Step 2: Substitute the expression of x in the other equation. In this case, substitute (5 + 2y) / 3 for x in equation (2):
2y - 5((5 + 2y) / 3) = 9
Step 3: Simplify and solve for y. Multiply both sides of the equation by 3 to get rid of the fraction:
3(2y) - 5(5 + 2y) = 27
6y - 25 - 10y = 27
-4y - 25 = 27
-4y = 27 + 25
-4y = 52
y = 52 / -4
y = -13
Step 4: Substitute the value of y back into either equation to solve for x. Let's use equation (1):
3x - 2(-13) = 5
3x + 26 = 5
3x = 5 - 26
3x = -21
x = -21 / 3
x = -7
So the solution to the simultaneous equations is x = -7 and y = -13.
In your case, you mentioned that you already found x = -7. To substitute it into equation (1), you can simply replace x with -7:
3(-7) - 2y = 5
-21 - 2y = 5
-2y = 5 + 21
-2y = 26
y = 26 / -2
y = -13
So, you can see that when you substitute x = -7 into equation (1), you obtain the same value of y as we found earlier, which is -13.