Question

Find the solution to the system of equations using elimination by addition:

10x + 10y = 60
5x - 5y = 40
a) x = 10, y = 2
b) x = 7, y = -1
c) x = -7, y = 9
d) x = 7, y = 1

Answer 1

To solve the system of equations 10x + 10y = 60 and 5x - 5y = 40 using elimination by addition, we can add the equations together to eliminate the variable 'y' and solve for 'x'. The solution to the system of equations is x = 7 and y = -1.

Step-by-step explanation:

To solve the system of equations using elimination by addition, we will add the two equations together. This will eliminate the variable 'y', allowing us to solve for 'x'.

First, multiply the second equation by 2 to make the coefficients of 'y' the same in both equations:

10x + 10y = 60

10x - 10y = 80

Now, add the two equations together to eliminate 'y':

20x = 140

Divide both sides of the equation by 20 to solve for 'x':

x = 7

Now substitute the value of 'x' back into one of the original equations and solve for 'y':

10(7) + 10y = 60

70 + 10y = 60

Subtract 70 from both sides and divide by 10:

10y = -10

y = -1

Therefore, the solution to the system of equations is x = 7 and y = -1.