Solve this equation using substitution method a-2b=9 2a+3b=4
Isolate a for :
a - 2 b = 9
Add 2 b to both sides
a = 9 + 2 b
a = 2 b + 9
Put this value in equation:
2 a + 3 b = 4
2 ( 2 b + 9 ) + 3 b = 4
4 b + 18 + 3 b = 4
7 b + 18 = 4
Subtract 18 to both sides
7 b = - 14
b = - 14 / 7
b = - 2
Put this value in equation:
a - 2 b = 9
a - 2 ( - 2 ) = 9
a + 4 = 9
Subtract 4 to both sides
a = 5
The solutions to the system of equations are:
a = 5 , b = - 2
Well, since you're asking the Clown Bot, I hope you're prepared for a number of silly substitutions! Let's dive in!
First, let's solve the first equation, a - 2b = 9, for a.
Let's sub our clown friend Bob for b:
a - 2(Bob) = 9
This simplifies to:
a - 2Bob = 9
Now let's move on to the second equation, 2a + 3b = 4, and substitute Bob for b:
2a + 3(Bob) = 4
This one simplifies to:
2a + 3Bob = 4
Now, we need to solve for either a or Bob in one of the equations. Let's solve the first equation for a:
a = 9 + 2Bob
Now, we'll substitute that expression into the second equation:
2(9 + 2Bob) + 3Bob = 4
Simplifying further, we have:
18 + 4Bob + 3Bob = 4
Combining like terms:
7Bob + 18 = 4
To isolate Bob, we need to subtract 18 from both sides:
7Bob = -14
And finally, divide both sides by 7:
Bob = -2
Now that we know Bob, we can substitute back into the first equation to find a:
a - 2(-2) = 9
a + 4 = 9
Subtracting 4 from both sides, we find:
a = 5
So the solution to the system of equations is a = 5 and b = -2.
Remember, this was a Clown Bot's approach, so take it with a grain of silliness!
To solve the system of equations using the substitution method, we need to solve one equation for one variable and substitute that expression into the other equation. Let's solve the first equation for a:
a - 2b = 9
Adding 2b to both sides gives:
a = 9 + 2b
Now we can substitute this expression for a into the second equation:
2a + 3b = 4
Substituting a with 9 + 2b gives:
2(9 + 2b) + 3b = 4
Expanding the parentheses gives:
18 + 4b + 3b = 4
Combining like terms:
7b + 18 = 4
Next, we can isolate b by subtracting 18 from both sides:
7b = 4 - 18
Simplifying:
7b = -14
Finally, we solve for b by dividing both sides of the equation by 7:
b = -14/7
b = -2
Now that we have the value of b, we can substitute it back into the equation a = 9 + 2b to find the value of a:
a = 9 + 2(-2) = 9 - 4 = 5
Therefore, the solution to the system of equations is a = 5 and b = -2.
To solve this system of equations using the substitution method, we will solve one equation for one variable and substitute it into the other equation. Let's start with the first equation:
a - 2b = 9 ----(1)
Step 1: Solve equation (1) for 'a'
To isolate 'a', we can add 2b to both sides of the equation:
a = 9 + 2b ----(2)
Now, we will substitute this value of 'a' into the second equation:
2a + 3b = 4 ----(3)
Substitute the value of 'a' from equation (2) into equation (3):
2(9 + 2b) + 3b = 4
Simplify the equation:
18 + 4b + 3b = 4
Combine like terms:
7b + 18 = 4
Next, we will isolate 'b' by moving constants to the other side of the equation:
7b = 4 - 18
Simplify:
7b = -14
Step 2: Solve for 'b'
To solve for 'b', divide both sides of the equation by 7:
b = -14 / 7
Simplify:
b = -2
Now that we have the value of 'b', we can substitute it back into either equation (1) or equation (2) to find the value of 'a'.
Using equation (1):
a - 2(-2) = 9
Simplify:
a + 4 = 9
Subtract 4 from both sides:
a = 5
Therefore, the solution to the system of equations is a = 5 and b = -2.