How to solve an equation for y and x using two steps?
Algebraic techniques were going to be discussed, but at the moment, they were just going to practice solving for x and solving for y. All right, so one should remember that for any equation, it has to equal something, and they need to solve for y using the equal sign. The instructor proceeded to demonstrate a series of steps. First, the focus was solely on solving for x in the equation: 5(3x) plus 4y equals 15. The instructor highlighted the importance of understanding the operations involved, which included addition, subtraction, multiplication, and division.
The instructor then explained that when solving for a variable, it's crucial to begin by undoing addition or subtraction. In this specific case, the goal was to eliminate the addition of 4y, which required subtracting 4y from both sides of the equation. This yielded 3x equals 15 minus 4y. To remove the multiplication by the variable (3x), they needed to divide by three.
Next, the instructor emphasized that 15 and -4y could not be combined directly. However, when the equals sign was used, the equation was separated into two different fractions: 15 divided by 3, which simplified to 5, and -4/3y. This constituted the final solution for x.
Moving on to solving for y, the instructor reiterated that the goal was to eliminate the positive 3x term. Since there was no subtraction sign explicitly present, they decided to rearrange the equation to incorporate it. After subtracting 3x, the equation became 4y is not equal to 15 minus 3x. Finally, to undo the multiplication, the instructor separated the fractions, effectively solving for x and y in the given problem.