Elimination (Level 3)

Question

Solve the system of equations −3x+3y=15 and 5x−4y=−27 by combining the equations.

Answer 1

−3x+3y=15 and 5x−4y=−27

In order to solve by combining these equations, the coefficients for one of the variables must be either the same (you will subtract one from the other) or opposites (when you add them you will get zero)

-3x + 3y = 15

5x - 4y = -27

Let's eliminate the x. So we will multiply the first equation by 5 and the second equation by 3.

-15x + 15y = 75

15x - 12y = -81

Now add the 2 equations, combining like terms.

0x + 3y = -6

Divide by 3

y = -2

So, if we substitute the -2 for y into the first equation

-3x + 3(-2) = 15

-3x -6 = 15

add 6 to both sides

-3x = 21

Divide both sides by -3

x = -7

so, x = -7 and y = -2

(-7, -2)

To check, simply substitute these numbers into both equations and see if the answer is correct.

−3x+3y=15 and 5x−4y=−27

-3(-7) + 3(-2) = 15

21 - 6 = 15 TRUE

5(-7) - 4(-2) = -27

-35 + 8 = - 27 TRUE

So, (-7, -2) is the correct answer.

Hope this helps.

Answer 2

−3x+3y=15  multiply by 4 so -12x + 12y= 60 (1)

5x−4y=−27 multiply by 3 so 15x -12y = -81 (2)

now, add (1) and (2) to get: 3x = -21 or x = -7;

put -7 in -3x + 3y = 15 or 21 +3y = 15; 3y = -6 or y = -2;