Urgent! 50 points!

1. a graph of an equation in two variables or a function is a representation of an infinite number of solutions to the equation or function.

2. a system of equations may not have an exact solution that meets the conditions of a real-world solution.

3. using graphing technology is a very efficient way to find solutions to equations and systems of equations.
the intersection point of two graphed functions is the solution for a system of equations. it is the point that makes both equations true.

4. the intersection point of two graphed functions is the solution for a system of equations. it is the point that makes both equations true.

5. when two different functions f(x) and g(x) are graphed, the x-coordinate of the point of intersection is the solution to the equation formed from f(x) = g(x)

6. systems of equations may be a combination of linear and non-linear functions.

a table of values very rarely shows every possible solution to a system of equations. finding the approximate solution that is between two values on the table can be a good answer in many situations.

answer:

1%2ax%2b1%2ay=2

2%2ax%2b2%2ay=4

step-by-step explanation: lets start with the given system of linear equations

1%2ax%2b1%2ay=2

2%2ax%2b2%2ay=4

now in order to solve this system by using substitution, we need to solve (or isolate) one variable. i'm going to choose y.

solve for y for the first equation  

1%2ay=2-1%2axsubtract 1%2ax from both sides

y=%282-1%2ax%29 divide both sides by 1.  

which breaks down and reduces to  

y=2-1%2ax now we've fully isolated y

since y equals 2-1%2ax we can substitute the expression 2-1%2ax into y of the 2nd equation. this will eliminate y so we can solve for x.

2%2ax%2b2%2ahighlight%28%282-1%2ax%29%29=4 replace y with 2-1%2ax. since this eliminates y, we can now solve for x.

2%2ax%2b2%2a%282%29%2b2%28-1%29x=4 distribute 2 to 2-1%2ax

2%2ax%2b4-2%2ax=4 multiply

2%2ax%2b4-2%2ax=4 reduce any fractions

2%2ax-2%2ax=4-4 subtract 4 from both sides

2%2ax-2%2ax=0 combine the terms on the right side

0%2ax=0 now combine the terms on the left side.  

0=0 since this expression is true for any x, we have an identity.  

so there are an infinite number solutions. the simple reason is the 2 equations represent 2 lines that overlap each other. so they intersect each other at an infinite number of points.

first option

a function is a relation in which an input is paired with exactly one output.

so, let's find the right answer.

in our first option, our inputs are january, february, and march. the outputs are 30, 28, and 25. each input has it's own output. this is correct!

our second option we know is incorrect, because ms. valverade has two outputs, dogs and cats. this is not a function.

our third option is incorrect as well. the yellow square has two ouputs, the square and the triangle.

lastly, in our fourth option, we see the number 7 two times with a different output. therefore, this is not a function.

remember: each input must be paired with only one output!

a framing bias

step-by-step explanation:

rodrigo is subject to a framing bias i believe.