How do you solve the simultaneous equations 3x-4y=113x4y=11 and 5x+6y=125x+6y=12?

1 Answer
Aug 1, 2015

x=3x=3; y=-1/2y=12

Explanation:

You can solve this system of equations by using the multiplication method.

The first thing that you need to do is pick a variable to eliminate first, then figure out the least common multiple (LCM) of its coefficients.

Let's say that you want to eliminate xx and solve for yy first. The two coefficients of xx are 33 and 55, which means that they're LCM will be equal to 1515.

So, multiply the first equation by 55 and the second equation by -33 to get

5 * (3x - 4y) = 5 * 115(3x4y)=511

15x - 20y = 5515x20y=55

and

(-3) * (5x + 6y)= -3 * 12(3)(5x+6y)=312

-15x - 18y = -3615x18y=36

Add the left side and the right side of these two equations separately to get

color(red)(cancel(color(black)(15x))) - 20y - color(red)(cancel(color(black)(15x))) - 18y = 55 - 36

-38y = 19 => y = 19/(-38) = color(green)(-1/2)

Now use this value of y in one of the two equations to determine the value of x.

3x - 4(-1/2) = 11

3x + 2 = 11 => x = (11-2)/3 = color(green)(3)

The solutions to this system of equations are

{(x=3), (y=-1/2) :}