Answer the questions and complete the steps to solve the system of equations below.

2х + 3y = 13
x = 2
a) Which variable should you substitute for in the equation 2x + 3y = 13?
choose your answer...
b) What value can be substituted for that variable? choose your answer...
c) Rewrite the equation with the substitution. choose your answer...
d) Solve the equation for y.
e) Use substitution to check your solution for the system.

1 answer

Let's solve the system of equations step by step.

Given:

  1. \(2x + 3y = 13\)
  2. \(x = 2\)

a) Which variable should you substitute for in the equation \(2x + 3y = 13\)?

Answer: Substitute for \(x\).

b) What value can be substituted for that variable?

Answer: The value to substitute is \(2\) (since \(x = 2\)).

c) Rewrite the equation with the substitution.

Substituting \(x = 2\) into the equation \(2x + 3y = 13\):

\[ 2(2) + 3y = 13 \]

This simplifies to:

\[ 4 + 3y = 13 \]

d) Solve the equation for \(y\).

Now, we solve for \(y\):

  1. Subtract \(4\) from both sides:

\[ 3y = 13 - 4 \]

\[ 3y = 9 \]

  1. Divide by \(3\):

\[ y = \frac{9}{3} \]

\[ y = 3 \]

e) Use substitution to check your solution for the system.

We found \(x = 2\) and \(y = 3\). We will substitute these values back into the original equation to verify:

Check in \(2x + 3y = 13\):

\[ 2(2) + 3(3) = 4 + 9 = 13 \]

Since both sides are equal, our solution \(x = 2\) and \(y = 3\) is correct.

Summary of Answers:

a) \(x\)
b) \(2\)
c) \(4 + 3y = 13\)
d) \(y = 3\)
e) Verified, solution is correct.