How to solve system of equations
5a=5
6b-3c=15
2a+7c=-5
from the first
a = 1
replace a with 1 in the third that will give you c
then put the value of c into the 2nd to get b
first we will find the value of a that is a=1 tan we will put the value of a in eq3 to find c so on we wil find b by putting the value of c in eq2.
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To solve the system of equations:
1. Start by isolating one variable in one of the equations.
In this case, we can start with Equation 1: 5a = 5.
Divide both sides by 5: a = 1.
2. Substitute the value of the isolated variable into the other equations.
Substitute a = 1 into Equation 2: 6b - 3c = 15.
Simplify: 6b - 3c = 15.
3. Solve for one variable in terms of the other variable in Equation 2.
Add 3c to both sides: 6b = 3c + 15.
Divide both sides by 6: b = (3c + 15)/6.
4. Substitute the values of a and b into Equation 3: 2a + 7c = -5.
Substitute a = 1 and b = (3c + 15)/6 into Equation 3.
Simplify: 2(1) + 7c = -5.
5. Solve for the remaining variable, c.
Simplify Equation 4: 2 + 7c = -5.
Subtract 2 from both sides: 7c = -5 - 2.
Simplify: 7c = -7.
Divide both sides by 7: c = -7/7.
6. Substitute the value of c back into Equation 2 to solve for b.
Substitute c = -7/7 into Equation 2: 6b - 3(-7/7) = 15.
Simplify: 6b + 3 = 15.
Subtract 3 from both sides: 6b = 15 - 3.
Simplify: 6b = 12.
Divide both sides by 6: b = 12/6.
7. Simplify the values of a, b, and c:
a = 1
b = 2
c = -1
Therefore, the solution to the system of equations is a = 1, b = 2, c = -1.