Question 1169670: Solve the following pair simultaneously equations.
3/5x - 4y = -1
0.8x - 3.5y = 1/2 Found 2 solutions by Boreal, Theo:Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website! 0.6x-4y=-1
0.8x-3.5y=0.5
multiply everything by 10
6x-40y=-10
8x-35y=5
then top by 4 and bottom by -3
24x-160y=-40
-24x+105y=-15
-55y=-55
y=1
substitute back in to first 0.6x-4=-1, 0.6x=3, x=5
(5, 1)
check in the second 4-3.5=0.5
You can put this solution on YOUR website! if you have a calculator, then this is most easily done by using it.
you should save all intermediate results into a memory location so that as many of the decimal digits can be saved as possible.
your original equations are:
3/5 * x - 4 * y = -1
0.8 * x - 3.5 * y = 1/2
convert the equations to decimal form to get:
.6 * x - 4 * y = -1
.8 * x - 3.5 * y = .5
multiply both sides of the first equation by 7 and multiply both sides of the second equation by 8 to get:
4.2 * x - 28 * y = -7
6.4 * x - 28 * y = 4
subtract the first equation from the second to get:
2.2 * x = 11
solve for x to get:
x = 11/2.2 = 5
in the first equation, replace x with 5 to get:
3/5 * x - 4 * y = -1 becomes:
3/5 * 5 - 4 * y = -1 which becomes:
3 - 4 * y = -1
subtract 3 from both sides of the equation to get:
-4 * y = -4
solve for y to get:
y = 1
you have:
x = 5 and y = 1
replace x and y with those values in both the original equations to get:
3/5x - 4y = -1 becomes:
3/5 * 5 - 4 * 1 which becomes:
3 - 4 = -1 which becomes:
-1 = -1
this confirms the first equation is true when x = 5 and y = 1.
0.8x - 3.5y = 1/2 becomes:
.8 * 5 - 3.5 * 1 = 1/2 which becomes:
4 - 3.5 = 1/2 which becomes:
.5 = 1/2 which becomes:
1/2 = 1/2
this confirms the second equation is true when x = 5 and y = 1.
your solution is that x = 5 and y = 1
the graph of both equations is shown below.
the intersection point is at (x,y) = (5,1)
that confirms graphically that your solution is at x = 5 and y = 1.
