Since there are two variables, we have to get down to just one. Do this by solving one equation for one variable. The second equation, x+y-7=0 makes this easy to do.
- Add 7 and subtract y from both sides to get x=7-y.
Now we can use this expression to substitute for x in the other equation. Instead of 5x-3y-10=0, use (7-y) for x: 5(7-y) - 3y -10 = 0.
- Distributing the 5 and combining like terms, we get 35-8y=10, which solves to:
- y=25/8=3.125.
Plug the y value into either original equation to get x. Choosing the x=7-y form of the second equation, I get
x= 7-25/8. Get a common denominator to subtract the fractions or use a calculator:
- x= 56/8 - 25/8 = 31/8 = 3.875.
There's your answer! (3.875, 3.125)
I hope this helps, and happy mathing!
(Also, you can always just graph both equations on desmos.com and see where they intersect!)
Liz Z.
