Question

Solve the system of linear equations by elimination. Check your solution x+2y=13 -x+y=5

Answer 1

To solve the system of linear equations by elimination, let's add the two equations to eliminate one of the variables:

x + 2y = 13 (Equation 1)

-x + y = 5 (Equation 2)

Adding the two equations,

(x + 2y) + (-x + y) = 13 + 5

This simplifies to:

3y = 18

y = 18/3

y = 6

Substitute value of y into one of the equations, let's use Equation 2,

-x + 6 = 5

-x = 5 - 6

-x = -1

x = 1

So, the solution to the system of linear equations is x = 1 and y = 6.

Answer 2

The linear equations x+2y=13 and -x+y=5 are solved by elimination to get x=1 and y=6, which is verified by substituting these values back into the original equations.

Step-by-step explanation:

To solve the system of linear equations by elimination, we start with the given equations:

1. x + 2y = 13
2. -x + y = 5

Now, we will add the two equations together to eliminate the variable x:

(x - x) + (2y + y) = 13 + 5

This simplifies to:

0x + 3y = 18

With only one variable remaining, y, we can now solve for y:

y = 18 / 3

y = 6

To find the value of x, we substitute y=6 back into either one of the original equations. We'll use the second equation (-x + y = 5):

-x + 6 = 5

-x = -1

x = 1

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