Solve the following system of equations for the unknown variables.
a + b = 7
a + c = 12
b + c = 15
a + b = 7
a + c = 12
----------------subtract
b - c = - 5
then
b - c = -5
b + c = 15
----------- add
2 b = 10
b = 5
you take it from there
A+B=7, A=7-B---(1)
A+C=12,---(2), frm 1 substitute the value of A into eq 2 :7-B+C=12, C=12-7+B---(3)
also B+C=15---(4), also in the same way put C in eq3 into eq 4 ;B+12-7+B=15, B=5, now rem eq1 put B into it ;A=7-5=2 do the same thin 4 C by putin B in eq3 C=5
Sure, I can solve that for you. But first, let's spice things up with a joke related to solving systems of equations:
Why did the mathematician become a farmer?
Because he loved solving systems of cow-lations!
Now, let's get to solving the system of equations:
We can start by subtracting the first equation from the second equation to eliminate the "a" term:
(a + c) - (a + b) = 12 - 7
c - b = 5
Next, let's subtract the second equation from the third equation to eliminate the "c" term:
(b + c) - (a + c) = 15 - 12
b - a = 3
Now we have a system of two equations with two variables:
c - b = 5
b - a = 3
To solve this system, we can add the two equations together:
(c - b) + (b - a) = 5 + 3
(c - a) = 8
So, we can simplify this further to:
c = a + 8
Now, we can substitute this value of "c" into the second equation:
a + (a + 8) = 12
2a + 8 = 12
2a = 4
a = 2
Finally, we can substitute the value of "a" back into the first equation:
2 + b = 7
b = 5
So, the solution to the system of equations is:
a = 2
b = 5
c = 10
And that's how the numbers got all mixed up and finally found their places!
To solve the system of equations:
Step 1: Start with the first equation, a + b = 7.
Step 2: From the second equation, a + c = 12, isolate the variable a by subtracting c from both sides of the equation: a = 12 - c.
Step 3: Substitute the value of a into the first equation: (12 - c) + b = 7.
Step 4: Simplify the equation: b - c = -5.
Now we have two equations with two variables:
1) b - c = -5
2) b + c = 15
Step 5: Add the two equations together to eliminate the variable c: (b - c) + (b + c) = -5 + 15.
Step 6: Simplify the equation: 2b = 10.
Step 7: Divide both sides of the equation by 2 to solve for b: b = 5.
Step 8: Substitute the value of b in one of the original equations, e.g., b + c = 15: 5 + c = 15.
Step 9: Solve for c: c = 15 - 5 = 10.
Step 10: Substitute the values of b and c in one of the original equations to find the value of a. Let's use the first equation: a + b = 7.
Substituting the values: a + 5 = 7.
Solve for a: a = 7 - 5 = 2.
Therefore, the solution to the system of equations is a = 2, b = 5, and c = 10.
To solve this system of equations, we can use the method of substitution or elimination. Let's use substitution.
Step 1: Solve one equation for one variable
From the first equation, we can solve for variable "a":
a = 7 - b
Step 2: Substitute the value of "a" into the other equations
Now, substitute the value of "a" from step 1 into the second and third equations:
(7 - b) + c = 12
b + c = 15
Step 3: Solve the resulting equations
Simplify the second equation:
7 + c - b = 12
b + c = 15
You now have a system of two equations with two variables.
Now, we can use substitution or elimination to solve for the remaining variables.