Solve the following simultaneous equation 3a-b=10,2a+4b=0
multiply first one by 4
12 a - 4 b = 40
2 a + 4 b = 0
================ add
14 a = 40
a = 20/7
b = 3a - 10 = 60/7 - 70/7 = - 10/7
Yes
To solve the simultaneous equations 3a - b = 10 and 2a + 4b = 0, we can use the method of substitution or elimination. Let's use the method of substitution.
Step 1: Solve one equation for one variable in terms of the other variable.
From the first equation, we can solve for a in terms of b:
3a - b = 10
3a = b + 10
a = (b + 10)/3
Step 2: Substitute the expression for one variable into the other equation.
Substitute a with (b + 10)/3 in the second equation:
2((b + 10)/3) + 4b = 0
Step 3: Simplify and solve for b.
Multiply through by 3 to eliminate the fraction:
2(b + 10) + 12b = 0
2b + 20 + 12b = 0
14b + 20 = 0
14b = -20
b = -20/14
b = -10/7
Step 4: Substitute the value of b back into either equation to solve for a.
Let's substitute b = -10/7 back into the first equation:
3a - (-10/7) = 10
3a + 10/7 = 10
21a + 10 = 70
21a = 60
a = 60/21
a = 20/7
Therefore, the solution to the simultaneous equations is:
a = 20/7 and b = -10/7.
To solve the given simultaneous equations:
Equation 1: 3a - b = 10
Equation 2: 2a + 4b = 0
We can use the method of substitution or elimination. Let's use the substitution method:
Step 1: Solve Equation 1 for 'b':
3a - b = 10
-b = 10 - 3a
b = 3a - 10
Step 2: Substitute the value of 'b' in Equation 2:
2a + 4(3a - 10) = 0
2a + 12a - 40 = 0
14a - 40 = 0
14a = 40
a = 40/14
a = 20/7 or approximately 2.857
Step 3: Substitute the value of 'a' back into Equation 1 to find 'b':
3(20/7) - b = 10
60/7 - b = 10
-b = 10 - 60/7
-b = 70/7 - 60/7
-b = 10/7
b = -10/7 or approximately -1.429
So, the solution to the simultaneous equations is:
a = 20/7 or approximately 2.857
b = -10/7 or approximately -1.429