Solve by using the elimination method.
7x-8y=-20
8x+7y=74
To solve this system of equations using the elimination method, we will eliminate one of the variables by adding or subtracting the two equations.
Let's start by multiplying the first equation by 8 and the second equation by 7 to make the coefficients of x the same:
8 * (7x - 8y) = 8 * (-20)
7 * (8x + 7y) = 7 * 74
This simplifies to:
56x - 64y = -160
56x + 49y = 518
Now, we can subtract the second equation from the first equation to eliminate x:
(56x - 64y) - (56x + 49y) = -160 - 518
This simplifies to:
-113y = -678
Dividing both sides of the equation by -113:
y = -678 / -113
y = 6
Now, substitute the value of y back into either of the original equations. Let's use the first equation:
7x - 8(6) = -20
7x - 48 = -20
7x = 28
Dividing both sides of the equation by 7:
x = 4
Therefore, the solution to the system of equations is x = 4 and y = 6.
To solve this system of equations using the elimination method, we need to eliminate one of the variables by adding or subtracting the equations together. The goal is to create a new equation that only contains one variable, which we can then solve for.
In this case, we can eliminate the variable "x" by multiplying the first equation by 8 and the second equation by 7 in order to create opposite coefficients for "x".
(8)(7x-8y) = (8)(-20) --> 56x - 64y = -160 (equation 1)
(7)(8x+7y) = (7)(74) --> 56x + 49y = 518 (equation 2)
Now, we can subtract equation 2 from equation 1 to eliminate the variable "x". The equation will look like this:
(56x - 64y) - (56x + 49y) = (-160) - (518)
-64y - 49y = -678
Combining like terms:
-113y = -678
Divide both sides of the equation by -113 to solve for "y":
y = -678 / -113
y = 6
Now that we have the value of "y", we can substitute it back into one of the original equations to solve for "x". Let's use the first equation:
7x - 8(6) = -20
7x - 48 = -20
Add 48 to both sides of the equation:
7x = 28
Divide both sides of the equation by 7 to solve for "x":
x = 28 / 7
x = 4
Therefore, the solution to the system of equations is x = 4 and y = 6.
7x-8y=-20
8x+7y=74
Multiply the first equation by 7 and the second equation by 8.
49x -56y = -140
64x + 56y = 592
Now add the last two equations to eliminate y.
113 x = 452
X = 4
Now solve for y.