Let's solve the system of equations step by step.
Given:
- \(2x + 3y = 13\)
- \(x = 2\)
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 \(y\):
- Subtract \(4\) from both sides:
\[ 3y = 13 - 4 \]
\[ 3y = 9 \]
- 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.