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2a + b-C=-17 a + 5b - 3c = -13 3a-2b + 6C = 28solve by substitution

User Markshep
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1 Answer

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In order to solve for a set of three equations with three variables, you start by picking any two of the three sets of equations. That means you can pick equations 1 and 2, then 1 and 3, or 2 and 3. You now eliminate one of the variables from each pair using the elimination method.

We shall begin with equations 1 and 2.

2a + b - c = -17 -----------(1)

a + 5b - 3c = -13 --------(2)

Multiply equaton (1) by 1 and then equation (2) by 2, to eliminate the a variable. You now have;

2a + b - c = -17 --------(3)

2a + 10b - 6c = -26 ---(4)

Next you subtract equation (3) from equation (4)

9b - 5c = -9

We shall now move onto equations 2 and 3.

a + 5b - 3c = -13 ----------------(1)

3a - 2b + 6c = 28 --------------(2)

Multiply equation (1) by 3 and then equation (2) by 1 to eliminate the a variable. You now have;

3a + 15b - 9c = -39 ----------------(3)

3a - 2b + 6c = 28 ------------------(4)

Next you subtract equation (3) from equation (4)

-17b +15c = 67

We now have two new equations which are as follows;

9b - 5c = -9 -----------------(a)

-17b + 15c = 67 -------------(b)

We shall now solve for variables b and c by using elimination method. To begin, multiply equation (a) by 15 and equation (b) by -5 to eliminate the c variable.

135b - 75c = -135 ----------(1)

85b -75c = -335 -----------(2)

Subtract equation (2) from equation (1)

50b = 200

Divide both sides of the equation by 50 and you'll have,

b = 4

Next you substitute for the value of b into equation (a) which is one of the two new equations we just derived and you now have;

9b - 5c = -9

9(4) -5c = -9

36 - 5c = -9

Subtract 36 from both sids of the equation and you now have

- 5c = - 45

Divide both sides of the equation by - 5 and you now arrive at,

c = 9

Having calculated b = 4 and c = 9, we shall now go back to the "ORIGINAL" equations which are,

2a + b - c = -17 ------------------(1)

a + 5b - 3c = -13 ----------------(2)

3a - 2b + 6c = 28 --------------(3)

Substitute for the values of b and c into ANY of the equations, and so we shall take equation (1),

2a + b - c = -17

2a + 4 - 9 = -17

2a - 5 = -17

Add 5 to both sides of the equation,

2a = -12

Next you divide both sides of the equation by 2 and you arrive at,

a = - 6

Therefore your answer is,

a = - 6

b = 4

c = 9

User Yensy
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