Question

what is the point of intersection if this linear system: x+3y=7 and 2x+5y=12

Answer 1

Okay so you want to be find the point where they equal each other (the point where the y values and the x values of the graphs correspond). To do this we have to solve a simultaneous equation which means either adding or subtracting one equation from the other so that only one variable will remain (in this case x or y). For this to happen either the x or the y values must occur an equal number of times; i.e. x - y = 9 and x + 4y = 8 have the some number of x values in them (one).

Now you have two equations with different amounts of variables so you need to either divide or multiply one of them to produce (preferably) bunch of whole number before the variable and a whole number as the constant as well. The easiest option with the equations you got is to multiply by two, giving 2x + 6y = 14

subtracting:

2x + 6y = 14
- 2x + 5y = 12
--------------
y = 2

Which gives you your first value! As all three equations will give you the same x values when you put in the y value it is easy to find the x value:

2x + 5(2) = 12
2x = 2
x = 1

You can check the answer by inputting the values in any one of the equations to see whether the answer is correct:

x + 3y = 7
1 + 6 = 7
7 = 7

Answer 2

Oh ok so the answer is (1,2)

Answer 3

yep

Answer 4

ok thank you so much

Answer 5

YW :)