Substitution Method Challenge: Solve for x and y in the System -x-2y=4, 3x+y=8

Q: Which equation should I solve for a variable first?

Choose the equation where a variable has a coefficient of 1 (like y in 3x + y = 8). This avoids fractions and makes the algebra cleaner!

Q: What if both variables have coefficients other than 1?

Pick the variable with the smallest coefficient in either equation. For example, if you see 2x or 3y, solve for the variable with coefficient 2 since it's easier to work with.

Q: How do I check if my solution is correct?

Substitute both values into both original equations. For $ x = 4, y = -4 $: First equation gives -4 - 2(-4) = 4 ✓, second gives 3(4) + (-4) = 8 ✓

Q: What if I get different answers when checking each equation?

This means you made an algebra error somewhere. Go back and check your distribution, combining like terms, and arithmetic. The solution must work in both equations!

System of Equations with Substitution Method

Find the value of x and and band the substitution method.

$\begin{cases} -x-2y=4 \\ 3x+y=8 \end{cases}$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve the system of equations

00:06 Isolate Y

00:17 This is the expression for Y, substitute in the second equation to find X

00:32 Properly expand brackets, multiply by each term

00:41 Isolate X

00:49 Collect like terms

01:01 This is the value of X

01:05 Now substitute the value of X to find Y

01:25 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Find the value of x and and band the substitution method.

$\begin{cases} -x-2y=4 \\ 3x+y=8 \end{cases}$

Step-by-step solution

Let's begin by solving the system of equations using the substitution method.

First, solve the second equation for $y$ :

$3x + y = 8$

Solve for $y$ :

$y = 8 - 3x$

Next, substitute this expression for $y$ in the first equation:

$-x - 2(8 - 3x) = 4$

Distribute the $-2$ :

$-x - 16 + 6x = 4$

Combine like terms:

$5x - 16 = 4$

Add 16 to both sides:

$5x = 20$

Divide by 5:

$x = 4$

Now, substitute $x = 4$ back into $y = 8 - 3x$ to find $y$ :

$y = 8 - 3(4)$

$y = 8 - 12$

$y = -4$

Therefore, the solution to the system of equations is $(x, y) = (4, -4)$ .

Thus, the values of $x$ and $y$ are $x = 4$ and $y = -4$ .

Final Answer

$x=4,y=-4$

Key Points to Remember

Essential concepts to master this topic

Strategy: Solve one equation for a variable, then substitute
Technique: From 3x + y = 8, get y = 8 - 3x
Verification: Check both original equations: -4 - 2(-4) = 4 and 3(4) + (-4) = 8 ✓

Common Mistakes

Avoid these frequent errors

Substituting into the same equation used for isolation
Don't substitute y = 8 - 3x back into 3x + y = 8 = you get 3x + (8 - 3x) = 8, which simplifies to 8 = 8! This tells you nothing. Always substitute into the OTHER equation to find the variable value.

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

Which equation should I solve for a variable first?

Choose the equation where a variable has a coefficient of 1 (like y in 3x + y = 8). This avoids fractions and makes the algebra cleaner!

What if both variables have coefficients other than 1?

Pick the variable with the smallest coefficient in either equation. For example, if you see 2x or 3y, solve for the variable with coefficient 2 since it's easier to work with.

How do I check if my solution is correct?

Substitute both values into both original equations. For $x = 4, y = -4$ : First equation gives -4 - 2(-4) = 4 ✓, second gives 3(4) + (-4) = 8 ✓

What if I get different answers when checking each equation?

This means you made an algebra error somewhere. Go back and check your distribution, combining like terms, and arithmetic. The solution must work in both equations!

Can I solve for x first instead of y?

Absolutely! The substitution method works either way. However, solving for the variable with coefficient 1 (like y in this problem) usually involves less work.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 System of linear equations questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime