x is partly constant and partly varies with y.When y=5,x=19 and when y=10,x=34.
(i) Find the relationship between x and y.
(ii) Find x when y=7.
5*3+4=19
10*3+4=34
7*3+4=?
remember PEMDAS
7*3+4=25
7*3=21+4=25
Questions 1
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To find the relationship between x and y, we can observe that x is changing based on the value of y. Let's denote the constant part of x as a, and the varying part as b. Thus, the relationship between x and y can be expressed as:
x = a + by
We can find the values of a and b using the given information.
When y=5 and x=19, we can substitute these values into the equation:
19 = a + 5b ----(1)
Similarly, when y=10 and x=34, we can substitute these values into the equation:
34 = a + 10b ----(2)
Now we have a system of two equations with two variables (a and b). We can solve this system of equations to find the values of a and b.
To eliminate a, we can multiply equation (1) by 2, and equation (2) by -1:
2(19) = 2(a + 5b)
38 = 2a + 10b ----(3)
-(34) = -(a + 10b)
-34 = -a - 10b ----(4)
Adding equations (3) and (4) together, we get:
38 - 34 = 2a + 10b - a - 10b
4 = a
Now that we have the value of a, we can substitute it back into equation (1) to find the value of b:
19 = 4 + 5b
15 = 5b
b = 3
Therefore, the relationship between x and y is:
x = 4 + 3y
Now let's find the value of x when y=7. We can substitute y=7 into the equation obtained above:
x = 4 + 3(7)
x = 4 + 21
x = 25
So, when y=7, x=25.