Question

what is the solution to the system of equations ?5x - y = 40 y = 2x - 4A) (20, 12)B) (-20, 12) C) (12, -20) D) (12, 20)

Answer 1

We are to find the solution to the given system of equations.

`\begin{gathered} 5x\text{ - y = 40 -----------(i)} \\ y\text{ = 2x - 4 ------------(i}i) \end{gathered}`

We substitute for y in equation (i);

`\begin{gathered} 5x\text{ - y = 40} \\ 5x\text{ - (2x - 4) = 40} \\ 5x\text{ - 2x + 4 = 40} \\ 5x\text{ - 2x = 40 - 4} \\ 3x\text{ = 36} \\ (3x)/(3)\text{ = }(36)/(3) \\ \\ x\text{ = 12} \end{gathered}`

We are now to substitute for "x" in in equation (ii) ;

`\begin{gathered} y\text{ = 2x - 4} \\ y\text{ = 2 (12) - 4} \\ y\text{ = 24 - 4} \\ y\text{ = 20} \end{gathered}`

CONCLUSION:

The solution to the given system of equations is (12, 20).