5x-2y=14and 2x+2y=14

Answer 1

To solve this system of equations, you can use either elimination or substitution method.

Elimination Method:

To eliminate the variable "y", you can add the two equations together. This will eliminate the "y" terms and allow you to solve for "x".

5x - 2y + 2x + 2y = 14 + 14
7x = 28
x = 28/7
x = 4

Now substitute the value of "x" back into one of the original equations to solve for "y".

5(4) - 2y = 14
20 - 2y = 14
-2y = 14 - 20
-2y = -6
y = (-6)/(-2)
y = 3

So the solution to the system of equations is x = 4 and y = 3.

Substitution Method:

From the second equation, we can solve for "y" in terms of "x" by subtracting 2x from both sides:

2x + 2y = 14
2y = -2x + 14
y = (-2/2)x + 14/2
y = -x + 7

Now substitute this expression for "y" into the first equation:

5x - 2(-x + 7) = 14
5x + 2x - 14 = 14
7x = 14 + 14
7x = 28
x = 28/7
x = 4

Now substitute the value of "x" back into the expression for "y" that we found earlier:

y = -x + 7
y = -4 + 7
y = 3

So the solution to the system of equations is x = 4 and y = 3.