Question

Solve the following using the substitution method.
x=2y-5
3x-4y=-13

I know the answer is (-3,1), but I want to know how to get it.

Answer 1

Answer:

(-3,1)

Step-by-step explanation:

Equation: 3x - 4y = -13

1. We are given the clue : x = 2y - 5
2. Substitution Method means :

• We can plug 2y-5 in for x (because x = 2y - 5)

    3. Plug X into the equation (3x - 4y = -13):

• 3(2y-5) - 4y = -13
• Distribute (multiply the terms 2y and -5 by 3):
• 6y - 15 is the new term
• Write the rest of the equation
• 6y - 15 - 4y = -13
• Simplify (add the y terms first)
• (6y) + (-4y) will equal 2y
• Now we have
• 2y - 15 =  -13
• Add 15 to both sides
• 2y = -13 + 15
• Simplify
• 2y = 2
• Divide both sides by 2, and you will get:

  y = 1

   4. We plugged x into the equation to get y, now we can plug y into the equation to get x:

• 3x - 4(1) = -13
• 4(1) will equal 4 so we have :
• 3x - 4 = -13
• Add 4 to both sides to get :
• 3x = -9
• Divide both sides by 3 to get :

 X = -3

Now we have (-3, 1) , Good job! I hope this helps