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.

step-by-step explanation: