x+y=2 and 2x+7y=9

Question

Solve this system of equations

x+y=2

2x+7y=9

Answer 1

Hi! To solve for the values of x and y, it is best to solve for one of them first. So, let's convert the x to a y and solve for y.

Using the first formula,

x + y = 2

    -y   -y  (subtract y from both sides to isolate x)

    x  = 2 - y

Now, substitute the value of x (2 - y) into the second formula.

2x + 7y = 9

2(2 - y) + 7y = 9 

(multiply 2 * 2 and 2 * -y to get 4 – 2y)

4 – 2y + 7y = 9 

(combine the two y terms: -2 + 7 = 5)

 4 + 5y = 9    

-4          -4    (subtract 4 from each side to isolate 5y)

      5y = 5         

      ---   ---

      5     5    (divide both sides by 5 to isolate y)

       y = 1    

If y = 1, we can solve for the value for x using either formula, but let's use the simpler one.

x + y = 2

x + 1 = 2

x = 1

To further test that x = 1 and y = 1, we can substitute those values into the second formula to ensure it adds up correctly.

2x + 7y = 9

2(1) + 7(1) = 9

2 + 7 = 9

So, we have verified that x = 1 and y = 1!

Answer 2