Question

Solve the system, or show that it has no solution. If the system has infinitely many solutions, express them in the ordered-pair form given. {x+3y=5 {2x-y=3

Answer 1

To solve the given system of equations, first solve one equation for one variable in terms of the other variable. Then, substitute this expression into the other equation and solve for the remaining variable. Finally, substitute the value of the variable back into either of the original equations to find the value of the other variable.

Step-by-step explanation:

To solve the given system of equations:

1. Start by solving one of the equations for one variable in terms of the other variable. Let's solve the second equation for x:

2x - y = 3

=> 2x = y + 3

=> x = (y + 3)/2

1. Substitute this expression for x into the first equation:

x + 3y = 5

=> (y + 3)/2 + 3y = 5

1. Simplify the equation and solve for y:

(y + 3 + 6y)/2 = 5

=> (7y + 3)/2 = 5

=> 7y + 3 = 10

=> 7y = 7

=> y = 1

1. Substitute the value of y back into either of the original equations to find the value of x:

x + 3(1) = 5

=> x + 3 = 5

=> x = 2

Therefore, the solution to the system of equations is x = 2 and y = 1. This can be expressed in ordered-pair form as (2, 1).