can someone help in finding the ordered pair for this equation.
7x-9y=63
9y-7x=-63
7X - 9Y = 63
-7X + 9Y = -63
m1 = -A/B = -7 / -9 = 7/9.
m2 = 7/9.
m1 = m2 = 7/9.
Threfore, the lines are parallel and
has no solution. Solve the Eqs and
you'll get 0 = 0.
Put it in another way, the lines are coincident and parallel, so they are consistent and we have an infinite number of solutions (at every point where the two lines overlap).
Given:
7X-9Y=63
Let t be any real number equal to X, then
X=t
Y=(7t-63)/9
where -∞<t<∞
So if we multiply the 2nd Eq by -1, we'll notice that the 2 Eqs are exactly identicak.
Thanks!
To find the ordered pair for this equation, you can use substitution or elimination method. Let's solve it using the substitution method:
1. Begin with the two given equations:
7x - 9y = 63 (Equation 1)
9y - 7x = -63 (Equation 2)
2. Solve Equation 1 for x:
7x = 9y + 63
Divide both sides by 7:
x = (9y + 63) / 7
3. Substitute the value of x from Equation 1 into Equation 2:
9y - 7((9y + 63) / 7) = -63
Simplify:
9y - 9y - 63 = -63
-63 = -63
4. Since the equation simplifies to -63 = -63, this means that the two equations are equivalent to each other. Therefore, the given equations represent the same line.
In this case, there are infinitely many ordered pairs (x, y) that satisfy the equation since the two equations represent the same line. Any point on this line can be considered as a solution.