Question

What is the solution (using substitution) of the following equations? 2x+y=20 6x-5y=12

Answer 1

Y has a coefficient of 1 in the first equation, so it is easiest to use that one to write an expression for y.

... y = 20 - 2x . . . . . subtract 2x

Now, this expression can be substituted for y in the second equation.

$6x-5(20-2x)=12\qquad\text{substituted for y}\\6x-100+10x=12\qquad\text{eliminate parentheses}\\16x=112\qquad\text{add 100}\\\\x=\dfrac{112}{16}=7\qquad\text{divide by the x-coefficient}$

Then, using the expression for y, we find its value

... y = 20 -2·7 = 6

The solution of the equations is (x, y) = (7, 6).