system of Equation with fractions?

Question

4/10a + b =19
1/10a - b = 1
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whats the easiest way to do this?

I got a=10 but when I tried to find b I couldnt cancel out the a's.

BBall Thanks, I got get it now.

arrrg. I understand it now.

Chucky I was wondering if multiplying the equations by 10 would work, thanks.

Answer 1

multiplying by 10 eac equation you get:
4a +10b=190
a - 10b = 10

adding the firs to the second:

5a = 200



so a = 200/5 a = 40

and then


40 - 10b = 10
10b= 30
b = 3

check the in the equations by sustituying

Answer 2

The easiest way is to multiply both equations by 10, so you have
4a + 10 b = 190
a - 10 b = 10
Now add the two equation, you get

5a = 200
a = 200/5
a = 40
Substitute a = 40 in any of the two equations you get

40 - 10 b = 10
- 10 b = - 30
b = 3
There you go !!

Answer 3

Add both equations to cancel out the b's

This gives you 1/2 a = 20
Divide both sides by 1/2, giving you a = 40

Sub a = 40 in the first equation
4/10 * 40 + b = 19
16 + b = 19
b = 3

Therefore the solution is a = 40 and b = 3

We can also check to see if this is right by substituting the values back into the original equations:

4/10 (40) + 3 = 19
1/10 (40) - 3 = 1

Since both work out perfectly, we know it is correct!

Hope I helped

Answer 4

When your solving systems you have to take one of the equations and solve for one variable as a first step:

(1/10)a-b=1
b=(1/10)a-1 (just moved b to the other side and the 1 to the left side)

so now that we know what b equals we can plug it in to the other formula:

(4/10)a+(1/10)a-1=19 (now we can solve for a)
(5/10)a=20
(1/2)a=20 (divide both sides by 1/2 to isolate a)
a=20/(1/2) (a number divided by a fraction is the same as the same number multiplied by the reciprical of that fraction)
a=20(2/1)
a=40

Now that we have a we can plug it into either of the two formulas and find b:

(4/10)(40)+b=19
160/10+b=19
16+b=19
b=19-16
b=3

To check our answers we can plug in both a=40 and b=3 into either equation and see if it results in equalling what it's suppose to.

equation 1: (4/10)(40)+3 should equal 19
160/10+3=19
16+3=19

equation 2: (1/10)(40)-3 should equal 1
40/10-3=1
4-3=1

So we see it is true that a=40, and b=3
(it's always a good idea to check after when you're done)

Good luck man, math is really cool once you get into it :)

Answer 5

the easiest way to do this problem is to add the equations together, since the b's will cancel out.
by adding the equations you get
5/10a = 20
i am assuming that a is in the numerator (5/10)a, so a = 40
plugging a back into either equation (i am using the bottom equation arbitrarily) yeilds
(1/10)*40 - b = 1
4 - b = 1
b = 3

As a way to check your work, when you plug a and b into the first equation, everything works out perfectly.

hope this was helpful

Answer 6

I can't tell if this is (4/10) * a or 4/(10*a).
The first one:

(4/10) * a + b = 19
4*a + 10*b = 190

(1/10)*a - b = 1
a - 10*b = 10
- a + 10*b = -10

10*b = 190 - 4*a
10*b = -10 + a
190 - 4*a = -10 + a
200 = 5*a
a = 40

(1/10)a - b = 1
4 - b = 1
b = 3

Answer 7

4/10a + b + 1/10a - b = 20
5/10a = 20
a=40
b=3