https://file.aiquickdraw.com/mathbot/file/1726312219691yz269jmb.jpg

Let's break down the given system of linear equations:

1. \( 3x + 4y = 6 \)
2. \( -2x + 5y = -19 \)

First, the problem asks for the first equation to be solved in the form \( y = \dots \). Let's isolate \( y \) in the first equation.

Starting with the first equation:
\[
3x + 4y = 6
\]
Subtract \( 3x \) from both sides:
\[
4y = 6 - 3x
\]
Now, divide everything by 4:
\[
y = \frac{6 - 3x}{4}
\]
This is the first equation in the form \( y = \dots \).

Next, let's substitute this expression for \( y \) into the second equation to find the value of \( x \).

The second equation is:
\[
-2x + 5y = -19
\]
Substitute \( y = \frac{6 - 3x}{4} \) into this equation:
\[
-2x + 5\left( \frac{6 - 3x}{4} \right) = -19
\]
Now, simplify and solve for \( x \).

I'll calculate the solution now.It seems like I can’t do more advanced data analysis right now. Please try again later.

Would you like me to guide you through solving the system manually, or would you prefer to wait and try again?

Here are 5 related questions to expand on this:
1. What is substitution and how is it used in solving systems of equations?
2. Can you explain how to solve a system of equations graphically?
3. What does it mean if two lines (representing equations) are parallel when solving a system?
4. What is the determinant in a system of equations, and how does it relate to solutions?
5. How would you solve this system using matrix methods?

**Tip:** Always simplify your equations step-by-step to avoid mistakes when isolating variables!

Solve the system of linear equations: 3x + 4y = 6, -2x + 5y = -19. First equation solved in the form y = ?.

Learn how to solve a system of linear equations: 3x + 4y = 6 and -2x + 5y = -19. This guide demonstrates the substitution method, showing how to isolate variables and find solutions for both x and y. Ideal for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation