answer this simultaneous equation please. 3a-b=9 2a+2b=14
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Sure, let's solve these equations! I hope you're ready for a mathemagical journey.
Step 1: Let's solve the first equation, 3a - b = 9, for a:
3a = 9 + b
a = (9 + b)/3
Step 2: Now, we substitute this value of a into the second equation, 2a + 2b = 14:
2((9 + b)/3) + 2b = 14
(18 + 2b)/3 + 2b = 14
Step 3: Let's simplify this fraction situation by multiplying every term by 3 to get rid of the fraction:
18 + 2b + 6b = 42
8b = 42 - 18
8b = 24
Step 4: Divide both sides by 8 to solve for b:
b = 24/8
b = 3
Step 5: Now that we have the value of b, we can substitute it back into the first equation to solve for a:
3a - 3 = 9
3a = 9 + 3
3a = 12
a = 12/3
a = 4
Voila! The solution to the simultaneous equations is a = 4 and b = 3. Keep in mind that my mathematical journey might be a bit clowny, so double-check my steps to be sure!
To solve the simultaneous equations, you can use the method of substitution or elimination. I will demonstrate 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 = 9
3a = b + 9
a = (b + 9)/3
Step 2: Substitute the expression found in Step 1 into the other equation.
Substitute a = (b + 9)/3 into the second equation:
2a + 2b = 14
2[(b + 9)/3] + 2b = 14
Step 3: Simplify the equation and solve for b.
Multiply both sides of the equation by 3 to eliminate the fraction:
2(b + 9) + 6b = 42
2b + 18 + 6b = 42
8b + 18 = 42
8b = 42 - 18
8b = 24
b = 24/8
b = 3
Step 4: Substitute the value of b back into one of the original equations to solve for a.
Let's use the first equation:
3a - b = 9
3a - 3 = 9
3a = 9 + 3
3a = 12
a = 12/3
a = 4
So, the solution to the simultaneous equations is a = 4 and b = 3.
To solve the simultaneous equations:
3a - b = 9 (Equation 1)
2a + 2b = 14 (Equation 2)
You can use the method of substitution or elimination. Here, let's solve it using the substitution method:
Step 1: Solve Equation 1 for a or b
From Equation 1, rearrange it to solve for a:
3a - b = 9
=> 3a = b + 9
=> a = (b + 9) / 3
Step 2: Substitute the expression for a in Equation 2
Substitute the value of a from Step 1 into Equation 2:
2((b + 9) / 3) + 2b = 14
Step 3: Solve for b
Simplify the equation:
(2b + 18) / 3 + 2b = 14
Multiply all terms by 3 to remove the fraction:
2b + 18 + 6b = 42
Combine like terms:
8b + 18 = 42
Subtract 18 from both sides:
8b = 42 - 18
8b = 24
Divide by 8:
b = 24 / 8
b = 3
Step 4: Find the value of a
Substitute the value of b into either Equation 1 or Equation 2:
3a - 3 = 9
3a = 9 + 3
3a = 12
a = 12 / 3
a = 4
The solution to the simultaneous equations is a = 4 and b = 3.
Double the first one to get:
6a - 2b = 18
Now add the second equation,
2a + 2b = 14
and you get
8a = 32
which requires that
a = 4
Use either of the first two equations to get b.
8 + 2b = 14
Take it from there.