Question

What is the first step to solve the following system of equations using substitution? 3x+y=15 5x-3y=11Divide the second equation by 3. Multiply the first equation by 3. Solve the first equation for y. Add the two equations together.

Answer 1

(4, 3)

Explanation:

#1. Isolate x:

3x + y = 15

y = 15 - 3x

Substitute and solve for x:

5x - 3y = 11

5x - 3(15 - 3x) = 11

5x - 45 + 9x = 11

5x + 9x = 11 + 45

14x = 56

x = 4

Substitute and solve for y:

y = 15 - 3x

y = 15 - 3(4)

y = 15 - 12

y = 3

Answer 2

• C. Solve the first equation for y

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Given system

• 3x + y = 15
• 5x - 3y = 11

If we are looking for substitution, then should solve one of the equations for one of the variables. This will allow us to substitute same into other equation and solve for the other variable.

Let's see what would be easy solution.

Equation 1

Solving for x is not straight away (we isolate x and divide all terms by its coefficient) as it has coefficient of 3.

Solving for y is easy, we just need to isolate it:

• 3x + y = 15 ⇒ y = - 3x + 15

Equation 2

Both of the variables have coefficients that are not factors of the constant term, so the easiest option is to solve the first equation for y.

This gives us the answer choice C.