Solve the system using any algebraic method.
22.)2x-5y=4 23.)5x+7y=12 24.)3x-4y=6
3x+4y=9 3x-2y=8 4x+7y=1
Thanks!
To solve the system of equations using any algebraic method, we can use substitution or elimination method.
Let's solve the system using the elimination method:
First, let's align the equations so that the x and y terms are in the same order:
22.) 2x - 5y = 4
3x + 4y = 9
23.) 5x + 7y = 12
3x - 2y = 8
24.) 3x - 4y = 6
4x + 7y = 1
Now, we can eliminate one variable by adding or subtracting the equations. We'll eliminate the variable "x".
Let's start with equations 22.) and 23.):
Multiply equation 22.) by 3 and equation 23.) by 2 to make the coefficients of "x" the same:
(3 * 2x - 3 * 5y) = (3 * 4)
(2 * 5x + 2 * 7y) = (2 * 12)
This simplifies to:
6x - 15y = 12
10x + 14y = 24
Now, we can eliminate the variable "x" by adding these two equations together:
(6x - 15y) + (10x + 14y) = 12 + 24
16x - y = 36 Equation (1)
Now, let's move on to equations 23.) and 24.):
Multiply equation 23.) by 3 and equation 24.) by 5 to make the coefficients of "x" the same:
(3 * 5x + 3 * 7y) = (3 * 12)
(5 * 3x - 5 * 2y) = (5 * 8)
This simplifies to:
15x + 21y = 36
15x - 10y = 40
Now, we can eliminate the variable "x" by subtracting these two equations:
(15x + 21y) - (15x - 10y) = 36 - 40
31y = -4
y = -4/31
Now that we have the value of y, we can substitute it back into equation (1) to find the value of x:
16x - (-4/31) = 36
16x + 4/31 = 36
16x = 36 - 4/31
16x = (36 * 31 - 4)/31
x = (1120 - 4)/496
x = 1116/496
x = 1113/496
Therefore, the solution to the system of equations is x = 1113/496 and y = -4/31.