Solve each system by substitution. See Example 1.
3y = 5x + 6
x + y = 2

Question

Solve each system by substitution. See Example 1.
3y = 5x + 6 
x + y = 2

Accepted Answer

Hey, everyone here we are asked to use the substitution method to solve the given system of equations. Five Y is equal to 12 X plus 15. And our second equation is X plus Y is equal to three. Here we have four and choice options. Answer choice A X is equal to zero and Y is equal to three. Answer B X is equal to three and Y is equal to zero answer C X and Y are equal to three and answer choice D no solution. So here to utilize the substitution method, we need to solve one of our equations for X and Y and then substitute in that expression into the other equation. So here we can easily solve for either X or Y by our second equation. Well, we can just choose to solve for X with this second equation. So that means we just want to subtract Y from both sides. So we have X is equal to three minus Y. And so now we just want to substitute in this expression into our first equation. And so doing this, we have five, Y is equal to 12 times the quantity of three minus Y plus 15. Now, we just want to distribute in this 12 into the set of parentheses here. So we have five, Y is equal to 36 minus 12 Y plus 15. Now, just combining like terms, we have five Y is equal to 51 minus 12 Y. And now we just want to move our Y terms to be on the same side of the equation. So we can simply add 12 Y to both sides of the equation. And so we now have 17, Y is equal to 51. And now solving for Y, we just need to divide both sides by its, by its coefficient which is 17. And so we have that our value for Y is simply equal to three. And so now we need to substitute in this value of Y that we obtained into our equation from earlier where we had X is equal to three minus Y. So now we will have X is equal to three minus our value for Y which is three and we know three minus three simplifies 20. So we found that X is equal to zero. So here we have found our value for X and our value for Y and we are left with answer choice. A where again, X is equal to zero and Y is equal to three. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Solve each system by substitution. See Example 1. 3y = 5x + 6 x + y = 2

Verified Solution

Key Concepts

Systems of Equations

Substitution Method

Linear Equations