How would I solve a system of linear equations x+y=2, 2x+7y=9 by using elimination

x = 1 & y = 1, so (1, 1)

Step-by-step explanation:

Hello! Here is my explanation:

First, you need to set the equations like this:

x + y = 2

2x + 7y = 9

Since you are using elimination, we need to cancel out one variable, either x or y. Let's cancel out x, since that is an easier one to work with since the 2nd equation has a 2 as x's coefficient, whereas there is a 7 as y's coefficient. To cancel out x, we need to multiply the 1st equation by 2, including the "= 2", so that it can be the same as the x in the 2nd equation. Like this:

2(x + y = 2)

2x + 7y = 9

Then, distribute the 2 to the whole equation. Multiply that 2 to the x, the y, and the 2 after that "=" sign, like this:

2x + 2y = 4

2x + 7y = 9

Now we are ready to eliminate! Since we now have the same x and coefficients for both equations, we can cancel them out. To do so, we need to subtract both equations. When we do that, we get 0 as a result for only the x, leaving us with only the y to solve. So we do 2x - 2x (which will be 0, so no need to write that 0), 2y - 7y, and 4 - 9. Like this:

 2x + 2y = 4

- 2x + 7y = 9

        -5y = -5

Next, we solve for y by dividing -5 on both sides, which will result in 1 being our y-value:

-5y = -5

-5      -5

y = 1

Now that we have our y-value of 1, we can plug that in for y in either one of our system of equations. It is always best and easiest to use the simplest equation with smaller numbers, so let's use the 1st equation, x + y = 2.

x + y = 2

x + 1 = 2

Now solve for x by subtracting 1 on both sides, which will result in 1 being out x-value:

x + 1 = 2

   - 1   -1

x = 1

So therefore, the solution to this system of equations is (1, 1). We used the method of elimination to solve this system. I hope this helps you understand how to approach these problems! Have a great day :)