solve using multiplication method: 8x-9y=-15 -4x=19+y
Strange way to type it, I read it as
8x-9y = -15
-4x = 19+y
I would double the 2nd:
-8x = 38+2y
or
8x + 2y = -38
8x - 9y = -15
subtract them
11y = -23
y = -32/11
sub into original 2nd
-4x = 19 - 23/11
-4x = 186/11
x = -186/44
x = -186/44 , y = -23/11
To solve the system of equations using the multiplication method, we need to eliminate one variable by multiplying both equations so that the coefficients of one variable are the same.
Let's start by multiplying the second equation by -1 to make the coefficient of x positive:
-1 * (-4x) = -1 * (19 + y)
This simplifies to:
4x = -19 - y
Now we have two equations to work with:
8x - 9y = -15
4x = -19 - y
To eliminate y, we will multiply both sides of the second equation by -9:
-9 * (4x) = -9 * (-19 - y)
This simplifies to:
-36x = 171 + 9y
Now we have two new equations:
8x - 9y = -15
-36x = 171 + 9y
Next, we can add the equations together to eliminate the y variable:
(8x - 9y) + (-36x) = (-15) + (171 + 9y)
Simplifying this equation gives:
8x - 9y - 36x = -15 + 171 + 9y
Combining like terms:
-28x - 9y = 156 + 9y
Now, we can solve for x:
-28x = 156 + 18y
Divide both sides by -28 to get x by itself:
x = - (156 + 18y) / 28
Simplifying this expression further is not possible until we have a specific value for y.
If you have a specific value for y, you can substitute it back into either of the original equations to solve for x.
To solve the given system of equations using the multiplication method, follow these steps:
Step 1: Rearrange the equations in the standard form (ax + by = c).
Given equations:
1) 8x - 9y = -15
2) -4x = 19 + y
To eliminate the variable "y," multiply equation 2) by 9.
3) -36x = 171 + 9y
Step 2: Now, we have equation 1) as 8x - 9y = -15 and equation 3) as -36x = 171 + 9y.
Step 3: Add equation 1) and equation 3) to eliminate the variable "y."
8x - 9y + (-36x) = -15 + (171 + 9y)
-28x = 156 + 9y
Step 4: Rearrange the equation to solve for "x" or "y".
-28x - 9y = 156 + 9y
-28x = 156 + 18y
-28x - 18y = 156
Step 5: Divide the whole equation by -2 to simplify it.
14x + 9y = -78 (Equation 4)
Step 6: Now, we have the following two equations:
1) 8x - 9y = -15 (Equation 1)
4) 14x + 9y = -78 (Equation 4)
Step 7: Add equation 1) and equation 4) to eliminate the variable "y".
(8x - 9y) + (14x + 9y) = -15 + (-78)
22x = -93
Step 8: Solve for "x" by dividing both sides of the equation by 22.
x = -93/22
Simplify if needed.
Step 9: Substitute the value of "x" back into either equation to solve for "y".
Let's use equation 1) to find "y".
8(-93/22) - 9y = -15
-744/22 - 9y = -15
-744 - 198y = -330
Step 10: Solve for "y."
-198y = -330 + 744
-198y = 414
Divide both sides by -198.
y = 414/-198
Simplify if needed.
Therefore, the solution to the system of equations is x = -93/22 and y = -207/99.