These problems are called systems of equations. Basically you have two linear equations and you need to find the values for x and y. In other words, all these equation are lines and our answer will be the exact point that the pair of lines intersect. For example, if we get x=1 and y=2 the lines will intersect at point (1,2). Now that you have some background knowledge here comes the tricks and tactics kid.
We know that we can solve one variable equation easily. For example...
x+1=2
x=1 obviously
Cause we have two variables x and y it is not possible to find a solution. For example, in the equation x+y=10, x=1 when y=9 and x=2 when y=8. There is not correct answer.
So what can we do? We have to make a two variable equation into a one variable equation.
There are two ways to do this: substitution and elimination. I will create a sample problem and then solve it using both methods.
x+y=2
2y-y=1
3)
-3x-5y=-7 -----> -12x-20y=-28
-4x-3y=-2 ------> -12x-9y=-6
-12x-20y=-28
-(-12x-9y=-6)
---------------------
-11y=-22
y=2
-3x-5(2)=-7
-3x=3
x=-1
4) 8x+4y=12 ---> 24x+12y=36
7x+3y=10 ---> 28x+12y=40
28x+12y=40
-(24x+12y=36)
---------------------
4x=4
x=1
8(1)+4y=12
4y=4
y=1
5) 4x+3y=-7
-2x-5y=7 ----> -4x-10y=14
4x+3y=-7
+(-4x-10y=14)
-------------------
-7y=7
y=-1
4x+3(-1)=-7
4x=-4
x=-1
6) 8x-3y=-9 ---> 32x-12y=-36
5x+4y=12 ---> 15x+12y=36
32x-12y=-36
+(15x+12y=36)
--------------------
47x=0
x=0
8(0)-3y=-9
-3y=-9
y=3
7)-3x+5y=-2
2x-2y=1 ---> x-y=1/2 ----> x=y+1/2
-3(y+1/2)+5y=-2
-3y-1.5+5y=-2
2y=-0.5
y=0.25
2x-2(0.25)=1
2x=1.5
x=0.75
Yes the graph does show a proportional relationship because each x value has only one y value
Monday to Friday is 5 days
$3.50 for 3 days + $2.00 for 2 days
=$5.50
Based on the data presented, it can be concluded out of the 52 females 26 prefer cats.
<h3>How to read the graph?</h3>
To read the graph we must take into account that the rows refer to the preference of men, preference of women and those who have no preference.
On the other hand, the columns refer to the number of students of both genders who prefer or do not prefer each animal. Additionally, adding all the students of each gender we have the total of the sample.
According to the above, the total sample of female students would be 52.
According to the above, the fraction that expresses this relationship correctly is:
Note: This question is incomplete because the graph is missing. Here is the graph.
Learn more about fraction in: brainly.com/question/10354322
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