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"Systems of Linear Magic"
DIRECTIONS
You are given the following system of equations. Answer the questions
below using this system.
1st Equation: 4x + y = 7
2nd Equation: 2x + y = 11
1.) Solve the system of equations by using the elimination method.
2.) Following the steps described in the "How to Create a Magic Potion"
section on page 1, let's brew a magic potion! Answer the following
questions about your "magic potion"equation.
A.) What is the factor that you have multiplied the 2nd equation by?
C.) What is the magic potion equation you have created?
3.) Using your newly created "magic potion" equation along with the original
2nd equation, solve this new system of equations by using the elimination
method.
4.) Why do you think this "magic potion" method works mathematically to
give us the exact same solution? Use at least 2 complete sentences.

Sagot :

The solution of the system of equations are x = -2 and y = 15, the factor is 2 and 4 for the 1st and 2nd equation respectively.

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have a system of equations:

1st Equation: 4x + y = 7

2nd Equation: 2x + y = 11

Subtract equation 2nd from 1st

(4x + y) - (2x + y) = 7 - 11

2x = -4

x = -2

Now in equation 1st multiply by 2 and in equation 2nd multiply by 4

8x + 2y = 14

8x + 4y = 44

Subtract:

-2y = -30

y = 15

The factor is 2 and 4 for the 1st and 2nd equation respectively.

Thus, the solution of the system of equations are x = -2 and y = 15, the factor is 2 and 4 for the 1st and 2nd equation respectively.

Learn more about the linear equation here:

brainly.com/question/11897796

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