Step-by-step explanation:
what don't you understand about this ? did you never solve 2 equations with 2 variables ?
it is really easy. there are 2 main approaches :
1. substitution. you use one of the two equations to express one variable by an expression purely in the other variable. then you use that in the other equation (resulting in one equation with one variable) and solve it. with that result you go back to the other equation and calculate the other variable.
2. equation arithmetic. when the terms of at least one of the variables are similar in both equations, you can multiply (if needed) one or both equations (left and right side !) by a fitting number and then add it subtract one equation from the other, so that you are left with one equation in one variable, which you solve. with that result you go back to any of the original equations and calculate the other variable.
there would be a third option for questions like this :
3. trial and error. simply put the point coordinates as x and y into both equations, and see for what point(s) both remain true.
but in order to show you the methodical approaches, we will use substitution for question 2 and equation arithmetic for question 3.
2)
2x + y = 5
-x + 2y = 5
I use the first equation to transform. and I get
y = 5 - 2x
with that I go into the second equation :
-x + 2(5 - 2x) = 5
-x + 10 - 4x = 5
-5x = -5
x = 1
and with that I get
y = 5 - 2×1 = 5 - 2 = 3
so, C (1, 3) is the right answer.
3)
2x + y = 7
-x + y = 1
let's subtract the second equation from the first :
2x + y = 7
- -x + y = 1
------------------
3x + 0 = 6
3x = 6
x = 2
with that I go into one of the original equations :
-2 + y = 1
y = 3
so, A (2, 3) is the right answer.
are all real numbers
we're translating the function horizontally, so the range remains the same
we're stretching the function horizontally, so the range doesn't change
we're translating the function 1 unit up, but the range is already all the real numbers, so it doesn't change.