Question

How do you solve using elimination of 2x + 5y =17 and 6x – 5y = -9 ?

Answer 1

Hint: To solve this question we will substitution one variable. From the equation $6x – 5y = -9$ we can get the value of 5y in terms of x and we will put it in the other equation. so the other equation will have only one variable that is x, then we can solve for both x and y.

Complete step by step solution:
The given equations are $2x + 5y =17$ and $6x – 5y = -9$
From the equation $6x – 5y = -9$ , we can say 5y is equal to $6x + 9$ . We can see that there is a term 5y in the equation 2x + 5y =17 We can replace the term 5y in the equation $2x + 5y = 17$.
So $2x + 6x + 9 = 17$
Further solving we get $8x + 9 = 17$
Adding 9 both sides we get $8x = 8$
So x is equal to 1
Now putting x equal to 1 in $2x + 5y =17$ we get $2 + 5y = 17$ , so the value of y is equal to 3. So $x=1$ and $y=3$ are the solution.

Note: We can check whether our is correct or not by putting the value of x and y in both the equations. By putting x equal to 1 and y equal to 3 in the equation in $2x + 5y =17$ we get $2 + 15=17$ which is correct. If we put $x=1$ and $y=3$ in $6x – 5y = -9$ we get $6 – 15= -9$ so $x=1$ and $y=3$ are correct solutions.