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

1 Answer
Aug 1, 2015

x=3; y=-1/2

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 x and solve for y first. The two coefficients of x are 3 and 5, which means that they're LCM will be equal to 15.

So, multiply the first equation by 5 and the second equation by -3 to get

5 * (3x - 4y) = 5 * 11

15x - 20y = 55

and

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

-15x - 18y = -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) :}