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solve system of equations using substitution

label Algebra
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3x-2y=10

3x+2y=14

Nov 21st, 2014

Hello there,

So you have the following equations: 3x - 2y = 10 and 3x + 2y = 14. Let's work with the first equation to isolate the x variable.

3x - 2y = 10

3x = 10 + 2y

x = 10/3 + 2y/3

So now we have,

x = 10/3 + 2y/3

3x + 2y = 14

Let's substitute the first equation into the second equation to get:

3x + 2y = 14

3(10/3 + 2y/3) + 2y = 14

30/3 + 6y/3 + 2y = 14

10 + 2y + 2y = 14

10 + 4y = 14

4y = 4

y = 1

Let's solve for the value of x now.

3x - 2y = 10

3x - 2(1) = 10

3x - 2 = 10

3x = 12

x = 4

So we have x = 4 and y = 1. Let's check our solutions.

First check,

3x - 2y = 10

3(4) - 2(1) = 10

12 - 2 = 10

10 = 10 (yay)

Second check,

3x + 2y = 14

3(4) + 2(1) = 14

12 + 2 = 14

14 = 14 (yay)

So our solution is (4, 1).

Hope this helps. Stay strong and math on!

Nov 21st, 2014

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