What is x and y in the system of equations 3x + 2y = 170 and 4x + 6y = 360
What is x and y in the system of equations 3x + 2y = 170 and 4x + 6y = 360?
One way to solve this is by "linear combinations" -- getting either the x-term or the y-term in
both equations to be the same and then either add or subtract.
I'm going to make the y-term (2y) of the first equation to be the same as the y-term of the second
equation (6y) by multiplying the first equation by 3:
3x + 2y = 170 ---> multiply by 3 ---> 9x + 6y = 510
4x + 6y = 360 4x + 6y = 360
subtract down the columns: 5x = 150
divide by 5: x = 30
Now, substitute that value back into the first equation:
3x + 2y = 170 ---> 3(30) + 2y = 170 ---> 90 + 2y = 170
2y = 80
y = 40