Question

solving systems by elimination (part 2)
lets think about why adding and subtracting equations work for solving systems of linear equations.

warm-up is it still true?
here is a true equation: \\(50 + 1 = 51\\).

1 perform each of the following operations and answer these questions: what does each resulting equation look like? is it still a true equation?
a. add 12 to each side of the equation.
b. add \\(10 + 2\\) to the left side of the equation and 12 to the right side.
c. add the equation \\(4 + 3 = 7\\) to the equation \\(50 + 1 = 51\\).

2 write a new equation that, when added to \\(50 + 1 = 51\\), gives a sum that is also a true equation.

3 write a new equation that, when added to \\(50 + 1 = 51\\), gives a sum that is a false equation.

Explanation:

Perform operations on the equation \(50 + 1 = 51\)

$$
LATEXBLOCK0
$$

Create an equation yielding a true sum

$$
LATEXBLOCK1
$$

Create an equation yielding a false sum

$$
LATEXBLOCK2
$$

Answer:

Question 1

a. Resulting equation: \(50 + 1 + 12 = 51 + 12\) (or \(63 = 63\)). It is still a true equation.
b. Resulting equation: \(50 + 1 + 10 + 2 = 51 + 12\) (or \(63 = 63\)). It is still a true equation.
c. Resulting equation: \(50 + 1 + 4 + 3 = 51 + 7\) (or \(58 = 58\)). It is still a true equation.

Question 2

New equation: \(2 + 3 = 5\)
Sum: \(50 + 1 + 2 + 3 = 51 + 5\) (which simplifies to \(56 = 56\), a true equation).

Question 3

New equation: \(2 + 3 = 9\)
Sum: \(50 + 1 + 2 + 3 = 51 + 9\) (which simplifies to \(56 = 60\), a false equation).