7x+2y=5 and 3y=16-2x
7x+2y=5 and 3y=16-2x solve each of the following systems
using the method of youre choice. However, you must show
an organize work.
We could solve both equations, but what would we have? We
would still have two equations. Each would show y in terms
of x, or x in terms of y. We still wouldn't know the values of
x or y. E.g., y = 16/3 - 2/3 x (the second equation)
When you are given two equations in the same problem, you
can be sure that you are supposed to solve them simultaneously,
to find the one unique pair of x,y values that will solve both equations.
Let's proceed with that thought in mind.
7x+2y=5 3y=16-2x -> rewrite the second: 2x + 3y = 16
We'll eliminate the y terms by subtracting one equation from
the other. To do that, the y terms must be the same.
3 * (7x+2y) = 3 * 5 21x + 6y = 15
2 * (2x + 3y) = 2 * 16 ( 4x + 6y = 32)
Subtract and get----> 17x = -17
17x = -17
x = -1
We will substitute that x value into the first equation.
7*(-1) +2y = 5
-7 + 2y = 5
2y = 12
y = 6
Finally, substitute both values, x and y, into the second equation.
3 * 6 = 16 - (2 * -1)
18 = 16 - (-2)
18 = 18
Now, you know that x=-1 and y=6 solves both equations at
the same time. This tells you that if you plot the two equations
on the same graph, you will have two lines that intersect at (-1, 6).
Read More: ...