I don't get how to solve linear systems by multiplying first

Question

10x-9y=46

-2x+3y=10

Answer 1

Answer:

x = 19 and y = 16

Original equations:

10x-9y=46

-2x+3y=10

Solution:

To use the elimination (addition) method, you first need to ensure the coefficients associated with the variable to be eliminated are the same in both equations.

In this situation, if you want to eliminate "x", for example, multiply the bottom equation by 5.

10x-9y=46 = > 10x - 9y = 46

5(-2x+3y)=10(5) => -10x + 15y = 50

1. Add equations together to eliminate the "x" variable:

6y = 96

2 Divide both sides by 6 to get y = 96/6 = 16

3 Substitute 16 for y in one of the original equations to get

10x - 9 (16) = 46 => 10x - 144 = 46

4 Add 144 to both sides to get 10x = 190.

5 Divide both sides by 10 to get x = 19

6 Test your answer by substituting "x" and "y" answers in one of the original equations.

-2(19)+3(16)=10 => -38 + 48 = 10 = > 10 = 10 so it is correct.

Answer 2

Multiplying an equation by anything still results in the same graph. What we want is opposite coefficients of either variable so they cancel out when you add the two equations. As you can see, if we multiply the 2nd equation by 5, you get -10x. Or, we can multiply by -3 and get -9y. Let's do the first.

10x - 9y = 46

-10x + 15y = 50

Adding the two equations together...

6y = 96

6y/6 = 96/6

y = 16

You got the rest!