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solve the system of equations. (20 points) 3x + y = 5 5x - 4y = -3

part a: use the substitution method to solve the system. show each step of the process to receive full credit. write the solution as an ordered pair. (10 points)

part b: use the elimination method to solve the system. show each step of the process to receive full credit. write the solution as an ordered pair. (10 points)

(1, 2)

Step-by-step explanation:

Substitution

Rearrange one of the two equations so that "y" is isolated, or by itself on one side of the equal sign.

3x + y = 5 => y = 5 - 3x

Substitute y for 5-3x in the other equation:

5x - 4y = -3

5x - 4(5 - 3x) = -3   Use the distributive property to expand

5x - 20 + 12x = -3   Collect like terms to simplify

17x - 20 = -3           Start isolating x

17x = -3 + 20

17x = 17                    Divide both sides by 17

x = 1

Substitute x = 1 into one of the equations to find "y"

3x + y = 5

3(1) + y = 5

3 + y = 5      Isolate y by subtracting 3 from both sides

y = 2

Therefore the solution is (1, 2).

Elimination

Multiply one of the equations so that in each equation, there is a common variable and coefficient.

Multiply 3x + y = 5 by 4. It becomes 12x + 4y = 20.

Add each of the terms to add the equations together:

.   12x + 4y = 20

+   5x - 4y = -3    If you add these two equations, the y variable is eliminated.

    17x      = 17      Divide both sides by 17 to isolate x

             x = 1

Substitute x=1 into any of the equations.

3x + y = 5

3(1) + y = 5

3 + y = 5      Rearrange to isolate y

y = 2

Therefore the solutions is (1, 2).

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