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Lesson Topics Discussion Quiz: Class Homework

Example1

Title: System of Linear Equations with Infinite Solutions

Grade Lesson s5-l7

Explanation: The best way to understand SAT-4 is by looking at some examples. Take turns and read each example for easy understanding.

Examples

Topics → Definition Example1

Solve the following system of equations:

15x + 21 y = 24 and 28 y = -20 x + 32.

Step: 1

The given system of equations are:

15x + 21y = 24 equation(1)

28 y = -20 x + 32 equation(2)

Explanation:

Here the given equation system are 15x + 21 y = 24 and 28 y = -21 x + 32.

Step: 2

Let’s solve for y in terms of x from equation(2): \$y = -20 x + 32 / (28)\$

Then simplify the above equation: \$(-5x + 8) / 7\$

Explanation:

Here the equation (2) is simplified in the y terms.

Step: 3

Now, let’s substitute this expression for y into equation(1): \$15x + 21(-5 x + 8/(7)) = 24\$

Now, solve for x: \$15x - 105 x /(7) + (168)/7 = 24\$

Then simplify: \$15x - 15x + 24 = 24\$

24 = 24

This equation doesn’t make sense, as it implies 24 = 24, which is always true. This indicates that the system of equations is dependent, meaning there are infinitely many solutions.

Explanation:

Then here we plug the y value simplify the equation and then solve for the x value. It implies 24 = 24 so it gives many more infinitely solutions.