Question

Use the method to solve the linear system: x + 2y = 7 and 3x - y = 14.

Answer 1

To solve the linear system, multiply the first equation by 3 to eliminate the x terms. Add the second equation to the modified first equation. Solve the resulting equation for either variable. Substitute the solution back into one of the original equations to find the other variable.

Step-by-step explanation:

To solve the linear system x + 2y = 7 and 3x - y = 14, we can use the method of elimination. Here are the steps:

1. Multiply the first equation by 3 to eliminate the x terms: 3(x + 2y) = 3(7) => 3x + 6y = 21
2. Add the second equation to the modified first equation: (3x + 6y) + (3x - y) = 21 + 14 => 6x + 5y = 35
3. Solve the resulting equation for either variable. Let's solve for x by isolating it: 6x = 35 - 5y => x = (35 - 5y)/6

Now we can substitute this expression for x into one of the original equations to solve for y. Let's use the first equation:

x + 2y = 7

(35 - 5y)/6 + 2y = 7

Simplify and solve for y:

35 - 5y + 12y = 42

7y = 7

y = 1

Substitute this value of y back into the expression for x:

x = (35 - 5(1))/6

x = 5/6

Therefore, the solution to the linear system is x = 5/6 and y = 1.