Solve the Basic Simultaneous Equations: x + y = 18, y = 13

Q: Why is this system so easy compared to others?

This system is already partially solved! When one equation directly gives you a variable's value (like $ y = 13 $), you just substitute it into the other equation.

Q: What if both equations had two variables?

Then you'd need to isolate one variable first! For example, from $ 2x + y = 10 $, you could get $ y = 10 - 2x $, then substitute.

Q: Do I always substitute into the first equation?

Not necessarily! Substitute the known value into whichever equation will help you find the unknown variable. Usually it's the more complex equation.

Q: How can I double-check my work?

Substitute both values back into both original equations. For this problem: $ 5 + 13 = 18 ✓ $ and $ y = 13 ✓ $

Substitution Method with Direct Variable Value

Solve the following equations:

$\begin{cases} x+y=18 \\ y=13 \end{cases}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve the system of equations

00:06 Substitute the given Y value, and solve for X

00:17 Isolate X

00:32 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following equations:

$\begin{cases} x+y=18 \\ y=13 \end{cases}$

Step-by-step solution

To solve the system of equations using substitution, follow these steps:

The system of equations given is: $\begin{cases} x + y = 18 \\ y = 13 \end{cases}$
Step 1: Extract the given value for $y$ from the second equation: $y = 13$ .
Step 2: Substitute $y = 13$ into the first equation: $x + 13 = 18$
Step 3: Solve for $x$ by subtracting $13$ from both sides of the equation: $x = 18 - 13$
Step 4: After the subtraction, we find: $x = 5$

Therefore, the solution to the problem is $x = 5$ and $y = 13$ .

Final Answer

$x=5,y=13$

Key Points to Remember

Essential concepts to master this topic

Substitution Rule: Replace variable with known value from second equation
Technique: Substitute y = 13 into x + y = 18 to get x + 13 = 18
Check: Verify solution: 5 + 13 = 18 and y = 13 ✓

Common Mistakes

Avoid these frequent errors

Solving the wrong equation first
Don't try to solve x + y = 18 without using y = 13 first = impossible to find unique values! This leaves you guessing values. Always use the equation that gives you a direct variable value first, then substitute.

Practice Quiz

Test your knowledge with interactive questions

Solve the following equations:

$\begin{cases} 2x+y=9 \\ x=5 \end{cases}$

FAQ

Everything you need to know about this question

Why is this system so easy compared to others?

This system is already partially solved! When one equation directly gives you a variable's value (like $y = 13$ ), you just substitute it into the other equation.

What if both equations had two variables?

Then you'd need to isolate one variable first! For example, from $2x + y = 10$ , you could get $y = 10 - 2x$ , then substitute.

Do I always substitute into the first equation?

Not necessarily! Substitute the known value into whichever equation will help you find the unknown variable. Usually it's the more complex equation.

How can I double-check my work?

Substitute both values back into both original equations. For this problem: $5 + 13 = 18 ✓$ and $y = 13 ✓$

What if I get a negative answer?

Negative solutions are completely valid! Always trust your algebra. Just make sure to double-check your arithmetic and verify by substitution.

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