solve the system by the elimination method
5x+5y=-7
7x-3y=19
Rewrite as:
15x + 15y = -21 and
35x - 15y = 57
Now add them. The y terms cancel.
50 x = 36
x = 36/50 = 18/25
(90/25) + 5y = -7 = -175/25
5y = -265/25
y = -53/25
To solve the system of equations using the elimination method, we need to eliminate one variable by adding or subtracting the equations.
Let's start by multiplying the first equation by 7 and the second equation by 5 to make the coefficients of x in both equations equal:
7*(5x+5y) = 7*(-7)
5*(7x-3y) = 5*(19)
This simplifies the equations to:
35x + 35y = -49
35x - 15y = 95
Now, we can subtract the second equation from the first equation:
(35x + 35y) - (35x - 15y) = -49 - 95
35x + 35y - 35x + 15y = -144
50y = -144
Divide both sides of the equation by 50 to solve for y:
y = -144/50
y = -2.88
Now, substitute the value of y back into any of the original equations. Let's use the first equation:
5x + 5(-2.88) = -7
5x - 14.4 = -7
5x = -7 + 14.4
5x = 7.4
Divide both sides of the equation by 5 to solve for x:
x = 7.4/5
x = 1.48
Therefore, the solution to the system of equations is x = 1.48 and y = -2.88.