3a+b=10, 2a+4b=0
3 a + b = 10
-
2 a + 4 b = 0
__________
3 a - 2 a + b - 4 b = 10 - 0
a - 3 b = 10
Add 3 b to both sides
a = 10 + 3 b
Substitute this value in one of equations ( never mind wich ). In this case in first equation.
3 a + b = 10
3 ( 10 + 3 b ) + b = 10
3 ∙ 10 + 3 ∙ 3 b + b = 10
30 + 9 b + b = 10
30 + 10 b = 10
Subtract 30 to both side
10 b = - 20
Divide both sides by 10
b = - 2
a = 10 + 3 b
a = 10 + 3 ∙ ( - 2 )
a = 10 - 6
a = 4
Solution:
a = 4 , b = - 2
Proof:
3 a + b = 10
3 ∙ 4 + ( - 2 ) = 10
12 - 2 = 10
10 = 10
2 a + 4 b = 0
2 ∙ 4 + 4 ∙ ( - 2 ) = 0
8 - 8 = 0
0 = 0
Use substitution,
from the first: b = 10-3a
into the second
2a+4b=0
2a + 4(10-3a) = 0
2a + 40 - 12a = 0
-10a = -40
a = 4
then b = 10-4b = 10-16 = -6
Mathematics
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A=4,b=-2
Well, it seems like those equations are not getting along very well. Maybe they just need a little counseling to find a common solution. Have you tried taking them out for a nice dinner or writing them a love song? Sometimes, a little romance can solve even the most complicated mathematical problems.
To solve this system of equations, we can use the method of substitution or elimination. Here's how you can solve it using the method of substitution:
Step 1: Solve one equation for one variable in terms of the other variable. Let's solve the first equation for 'a':
3a + b = 10
Subtract b from both sides:
3a = 10 - b
Step 2: Now, solve the second equation for 'b' in terms of 'a':
2a + 4b = 0
Subtract 2a from both sides:
4b = -2a
Divide by 4 on both sides:
b = -0.5a
Step 3: Substitute the expression for 'b' from the second equation into the first equation:
3a + (-0.5a) = 10
Simplify the equation:
2.5a = 10
Divide both sides by 2.5:
a = 4
Step 4: Substitute the value of 'a' back into the second equation to find 'b':
2(4) + 4b = 0
8 + 4b = 0
Subtract 8 from both sides:
4b = -8
Divide both sides by 4:
b = -2
Therefore, the solution to the system of equations is a = 4 and b = -2.