simultaneous equations
x + 2y = 4
3x - 4y = 7
x=3 and y = 1/2
i need to explain how i got this answer and do not know how to do that?
i am confused about how you got this answer what working out is it
the object in "elimination" is to get the coefficients of either the x or the y to be opposites, so that when you add the equations, they will cancel
so look at the first equation, if we multiply it by 2 we could have a 4y which is the opposite of -4y from the second equation.
let's do that
2x + 4y = 8 ....... the first times 2
3x - 4y = 7 ........ no change
------------
5x + 0 = 15 .........I added them
x=3 ..................I divided both sides by 5
now take that x value and substitute it back into the easier of the two original equation to get y = 1/2
To solve the simultaneous equations x + 2y = 4 and 3x - 4y = 7, you can use the method of elimination. The goal is to manipulate the equations so that when you add them, one variable will be eliminated.
First, let's modify the first equation by multiplying it by 2 to create a 4y term that is the opposite of the -4y term in the second equation. This gives us:
2(x + 2y) = 2(4)
which simplifies to:
2x + 4y = 8
The second equation remains the same:
3x - 4y = 7
Next, add the two equations together:
(2x + 4y) + (3x - 4y) = 8 + 7
which simplifies to:
5x + 0 = 15 (the y terms cancel each other out)
Simplifying further, we have:
5x = 15
To solve for x, divide both sides by 5:
x = 3
Now that we have the value of x, substitute it back into one of the original equations. Let's use the first equation x + 2y = 4:
3 + 2y = 4
Subtract 3 from both sides:
2y = 1
Finally, divide both sides by 2 to solve for y:
y = 1/2
So the solution to the simultaneous equations is x = 3 and y = 1/2.