Using the substitution method, what is the value of a in the solution to the system of equations below?
a=3b+7
4a+9b=70
4a+9b=70
4(3b + 7) + 9b = 70
12b + 28 + 9b = 70
21b = 70 - 28
21b = 42
b = 2
~~~~~~~~~~~~~~~~~~~~~~~~
a=3b+7
a = (3 * 2) + 7
a = 13
a=3b+7...eq (1)
4a+9b=70 or 4a=-9b+70...eq (2)
multiplying equation i by 3
3(a)=3(3b+7)...eq (1)
3a=9b+21...eq (3)
subtracting equation (2) from eq(3)
4a=-9b+70...eq(2)
3a=9b+21...eq (3)
a = 49
this is the value of a
To find the value of a using the substitution method, we can substitute the value of a from the first equation into the second equation and solve for b.
First, let's substitute a=3b+7 into the second equation:
4(3b+7) + 9b = 70
Next, distribute the 4 to both terms inside the parentheses:
12b + 28 + 9b = 70
Combine like terms:
21b + 28 = 70
Now, let's isolate the variable by subtracting 28 from both sides:
21b = 70 - 28
21b = 42
Finally, divide both sides by 21:
b = 42 / 21
Simplifying:
b = 2
Now that we have the value of b as 2, we can substitute it back into the first equation to find the value of a:
a = 3(2) + 7
a = 6 + 7
a = 13
Therefore, the value of a in the solution to the system of equations is 13.
To solve this system of equations using the substitution method, we'll start by solving the first equation for a in terms of b. Then, we'll substitute this expression for a into the second equation and solve for b. Finally, we'll use the value of b to find the value of a.
Given:
a = 3b + 7 ............... Equation 1
4a + 9b = 70 ................ Equation 2
Step 1: Solve Equation 1 for a.
a = 3b + 7
Step 2: Substitute the expression for a from Equation 1 into Equation 2.
4(3b + 7) + 9b = 70
Step 3: Simplify and solve for b.
12b + 28 + 9b = 70
21b + 28 = 70
21b = 42
b = 2
Step 4: Substitute the value of b into Equation 1 to find the value of a.
a = 3(2) + 7
a = 6 + 7
a = 13
Therefore, the solution to the system of equations is a = 13.