Math Problem Statement

What is the value of b_2 given that the first equation is 3x + 4y = -9, and the second equation is 2x - 6y = 5? Give the value of a_2 using the first equation 4x - 3x = -9 and second equation 2x - 5 = 6. Find the value of c_1 given that the first equation is 3x - 9y = 4, and the second equation is 2x + 5y = 6.

Solution

Let's go through each of the questions one by one from the image you provided.

Question 1:

Given:

  • First equation: 3x+4y=93x + 4y = -9
  • Second equation: 2x6y=52x - 6y = 5

We need to solve this system of equations to find the value of b2b_2.

Question 2:

Given:

  • First equation: 4x3x=94x - 3x = -9
  • Second equation: 2x5=62x - 5 = 6

We need to find the value of a2a_2 by solving this system.

Question 3:

Given:

  • First equation: 3x9y=43x - 9y = 4
  • Second equation: 2x+5y=62x + 5y = 6

We need to solve this system to determine the value of c1c_1.

Let me begin by solving the system of equations for each of the three questions. I'll show you the detailed steps.

I'll start with Question 1.For Question 1, solving the system of equations:

  1. 3x+4y=93x + 4y = -9
  2. 2x6y=52x - 6y = 5

We get:

  • x=1713x = -\frac{17}{13}
  • y=3326y = -\frac{33}{26}

Thus, the value of b2b_2 (which seems to correspond to the solution for yy) is 3326-\frac{33}{26}.

Now, let's proceed to Question 2.It seems like I can’t do more advanced data analysis right now. Please try again later.

Would you like me to explain how to approach solving Question 2 manually, or answer any other part of the problem? Let me know!

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Systems of Equations

Formulas

Standard form of linear equations: ax + by = c
Substitution and Elimination methods

Theorems

The system of linear equations can be solved using the substitution or elimination method

Suitable Grade Level

Grades 8-10