Question

solve x+5y=11 and -x+4y=7 using elimination​

Answer 1

Answer: (1, 2)

Concept:

There are three general ways to solve systems of equations:

1. Elimination
2. Substitution
3. Graphing

Since the question has specific requirements, we are going to use elimination

Solve:

Given expressions

x + 5y = 11

-x + 4y = 7

Add both equations together to elimination [x] variable

(x + 5y) + (-x + 4y) = 11 + 7

x - x + 5y + 4y = 18

9y = 18

Divide 9 on both sides

9y / 9 = 18 / 9

$\boxed{y=2}$

Find the x value

x + 5y = 11 ⇔ Given equation

x + 5(2) = 11 ⇔ Substitute values of y

x + 10 = 11 ⇔ Simplify by multiplication

x + 10 - 10 = 11 - 10 ⇔ Subtract 10 on both sides

$\boxed{x=1}$

Hope this helps!! :)

Please let me know if you have any questions

Answer 2

Answer:

Stack the two equations and add them together as if they were multi-digit numbers. That will eliminate the x and then you can solve for the y. Knowing y you can then go back and solve for x.

Step-by-step explanation:

x + 5y = 11

-x + 4y = 7

---------------- "Add" the equations above to get the equation below.

9y = 18

Now you can divide both sides by 9 to see that y is equal to 2.

Now that you know that y = 2 you can substitute y in either of the two original equations. I'll use the first.

x + 5(2)= 11

x + 10 = 11

x = 1