Math

QuestionSolve for 'x' and 'y' in the equation 9x+3y=219x + 3y = 21.

Studdy Solution

STEP 1

Assumptions1. The equation is linear in nature, i.e., the highest power of the variables 'x' and 'y' is1. . The equation is in the standard form Ax + By = C, where A, B, and C are constants.
3. We are looking for all possible solutions for the variables 'x' and 'y'.

STEP 2

The given equation is 9x+y=219x +y =21.

STEP 3

We can simplify the equation by dividing the entire equation by the greatest common divisor of9,3, and21, which is3.
9x+3y3=213\frac{9x +3y}{3} = \frac{21}{3}

STEP 4

implify the equation to get a reduced form.
3x+y=73x + y =7

STEP 5

Now we have a simpler equation to work with. We can solve this equation for 'y' to find the possible solutions for 'y' in terms of 'x'.
y=73xy =7 -3x

STEP 6

Now we have an equation in terms of 'y'. This equation tells us that for any value of 'x', we can find a corresponding value of 'y' that makes the equation true.For example, if we choose x =1, we can find the corresponding value of 'y' as followsy=3(1)=4y = -3(1) =4So, one possible solution is (x, y) = (1,4).

STEP 7

Similarly, we can choose different values for 'x' and find the corresponding values for 'y'.For example, if we choose x =2, we can find the corresponding value of 'y' as followsy=73(2)=1y =7 -3(2) =1So, another possible solution is (x, y) = (2,1).

STEP 8

In general, for any real number 'x', the corresponding value of 'y' can be found using the equation y=73xy =7 -3x. Therefore, the solution to the given equation is a set of all ordered pairs (x, y) such that y =7 -3x for all real numbers 'x'.

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