solve the system by the elimination method: 4x=5y+24
5x=4y+21
To solve by elimination, you need x and y on the same side of the equation.
For the first one, subtract 5y from both sides to get 4x - 5y = 24
For the second one, subtract 4y from both sides to get 5x - 4y = 21
You want to add these two equations to eliminate one variable. You have to do something to each equation before this can happen. Multiply the top equation by -5 and the bottom equation by 4. Be sure to multiply each term including the 24 and 21 by those numbers.
When you add, the x's will cancel out and you can solve for y. Once you find the value for y, substitute it back into one of the ORIGINAL equations to find x. Then be sure to check x and y in both of the original equations to make sure, you haven't made a mistake.
To solve the system of equations using the elimination method, follow these steps:
1. Rearrange both equations in the standard form: ax + by = c.
Equation 1: 4x - 5y = 24
Equation 2: 5x - 4y = 21
2. Choose an equation you want to eliminate one variable from. In this case, let's eliminate the "y" variable.
3. Multiply each term in Equation 1 by 4 and Equation 2 by 5 to make the coefficients of "y" the same and opposite:
Equation 1: 16x - 20y = 96
Equation 2: 25x - 20y = 105
4. Subtract Equation 1 from Equation 2:
(25x - 20y) - (16x - 20y) = 105 - 96
25x - 20y - 16x + 20y = 9
Simplifying the equation gives:
9x = 9
5. Solve for "x" by dividing both sides of the equation by 9:
9x/9 = 9/9
x = 1
6. Substitute the value of "x" back into one of the original equations. Let's choose Equation 1:
4(1) - 5y = 24
4 - 5y = 24
7. Solve for "y":
Subtract 4 from both sides:
-5y = 20
Divide both sides by -5:
y = -4
8. The solution to the system of equations is x = 1, y = -4.
Therefore, the solution to the system by the elimination method is x = 1, y = -4.