solve the elimination methods
4x-9y=18.5
7y-2x=-10.5
Rewrite the second equation
-2x + 7y = -10.5 Now double it.
-4x + 14y = -21
Now add that to the first of your equations
5y = -2.5
y = -0.5
4x + 4.5 = 18.5
4x = 14
x = 3.5
To solve the system of equations using the elimination method, follow these steps:
Step 1: Multiply one or both equations by a constant (if necessary) to make the coefficients of either x or y terms in one equation equal to the coefficients in the other equation. This will allow you to eliminate one of the variables by adding or subtracting the two equations.
Let's make the coefficients of the x terms equal in both equations. Multiply the second equation by 2, so the coefficient of x becomes -4:
Original equations:
4x - 9y = 18.5
7y - 2x = -10.5
After multiplying the second equation by 2:
4x - 9y = 18.5
-4x + 14y = -21
Step 2: Add or subtract the two equations to eliminate the x variable and find the value of y.
Add the two equations together:
(4x - 9y) + (-4x + 14y) = 18.5 + (-21)
The x terms cancel out:
-9y + 14y = -2.5
Combine like terms:
5y = -2.5
Step 3: Solve for y by dividing both sides of the equation by 5:
5y/5 = -2.5/5
y = -0.5
So, the value of y is -0.5.
Step 4: Substitute the value of y into either of the original equations to find the value of x.
Using the first equation:
4x - 9(-0.5) = 18.5
4x + 4.5 = 18.5
Subtract 4.5 from both sides:
4x = 14
Divide both sides by 4:
4x/4 = 14/4
x = 3.5
So, the solution to the system of equations is x = 3.5 and y = -0.5.