solve by the elimination method What is the solution of the system?
5x+5y=-7
7x-2y=19
solution is?____
there are infinitely many solutions ____
there is no solution?_____
To solve the system of equations using the elimination method, we need to eliminate one variable using a combination of addition and/or subtraction. Let's start by eliminating one of the variables.
First, let's manipulate the equations so that the coefficients of one of the variables are the same. We can do this by multiplying the entire equation by a constant.
Multiply the first equation by 2 and the second equation by 5 to make the coefficients of 'y' equal:
10x + 10y = -14 (Multiplying the first equation by 2)
35x - 10y = 95 (Multiplying the second equation by 5)
Now, add the two equations together:
(10x + 10y) + (35x - 10y) = (-14) + (95)
45x = 81
Divide both sides by 45 to solve for 'x':
x = 81/45
x = 9/5
Now that we have the value of 'x', substitute it back into one of the original equations to solve for 'y'. Let's use the first equation:
5(9/5) + 5y = -7
9 + 5y = -7
5y = -16
y = -16/5
Therefore, the solution to the system of equations is x = 9/5 and y = -16/5.
Since we have found specific values for both 'x' and 'y', there is a unique solution to the system.