Question

Given the system of equations, what is the solution?

2x + 3y = 2
3x - 4y = 20

Answer 1

solve either by substitution or by multiplying the first by 3/2 and subtracting that from the second to find y and then solve for x, or use a matrix method...

Answer 2

?

Answer 3

I will solve by elimination: multiply the first equation by 3/2 to get:
\[3x + \frac{9}{2}y = 3\]
comparing this with the second equation which is
\[3x - 4y = 20\]
we see that the coefficient of x (the number multiplying it) in both these equations is 3. So if we subtract one equation from the other (either will do) we will eliminate x and be left with an equation in y only which we can solve for y:
\[3x-4y -(3x + \frac{9}{2}y) = 20-3\]
\[-4y - \frac{9}{2}y = 17\]
\[-\frac{17}{2}y = 17\]
\[y=-2\]
Now substitute y=-2 into ANY one of your starting equations (it doesn't matter which one) to find x:
\[3x - 4(-2) = 20\]
\[3x = 20 - 8\]
\[3x=12\]
\[x=4\]

So x=4, y=-2