Part 1: Explain, in complete sentences, how you would use the substitution method to solve the following system of equations.

Part 2: Provide the solution to the system.

5x – y = –2
10x – 3y = –7

Question

Part 1: Explain, in complete sentences, how you would use the substitution method to solve the following system of equations.

Part 2: Provide the solution to the system.

5x – y = –2 
10x – 3y = –7

anonymous · Answer

First, solve for y in each equation.

5x - y = -2
-y = -2 - 5x
y = 5x + 2

10x-3y = -7
10x = -7 + 3y
10x+7 = 3y
y = (1/3)(10x+7)

Next, because each equation is set to equal y, they must be equal to each other. For example, if y = w and y = x, w must be equal to x.  Solve for x.

y = y
5x + 2 = (1/3)(10x + 7)
15x+6 = 10x+7
5x = 1
x=1/5

Now that you have a value of x, you can substitute x in for any of the two equations for the y-value. 

5x - y = -2
5(1/5) - y = -2
1 + 2 = y
y = 3

The solution to this system of equations is: (1/5, 3)

anonymous · Answer

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