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Given the equation 10x plus y equals 53 and knowing that x equals 5 and y equals 3 can someone explain the theory behind the steps to solve for x and y?
Wdonuts
10x + y = 53
Since this is a linear equation in two variables in the form ax + by = c, where a, b, and c are real numbers and a, b ≠0, the solution is any ordered pair (x, y) that makes the equation true such as (5, 3) is.
So that the question would be: "Is the point (5, 3) a solution of the equation 10x + y = 53 ?"
A solution of this equation is an ordered pair of real numbers with the following property:
When the x-coordinate is substituted for x and the y-coordinate is substituted for y in the equation, we obtain a true statement.
10x + y = 53 (substitute 5 for x, and 3 for y)
10(5) + (3) =? 53
50 + 3 =? 53
53 = 53 True
Thus, (5, 3) is a solution of the given equation.
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But what if you have to solve the equation as if you did not know what the values of x and y are (but that they will have to equal 5 and 3, respectively).
We can generate as many as ordered pair solutions as desired of y = -10x + 53, by substituting numbers for x and then finding the values for y.
You can make a table to obtain several ordered pair (x, y), which are solutions of the equation. For example use integer values of x from the set {-2, -1, 0, 1, 2, 3, 4, 5} to obtain eight ordered pairs.
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