Solve each system by substitution.
-2x = 6y + 18

Question

Solve each system by substitution.

-2x = 6y + 18

-29 = 5y - 3x

Accepted Answer

Hey, everyone. Here we are asked to use the substitution method to solve the given system of equations. Negative four X is equal to two Y plus 98. And the second equation is negative 100 154 is equal to three Y minus X. Here we have four answer choice options, answer a no solution answer B X is equal to one and Y is equal to negative 51 answer. C X is equal to seven and Y is equal to negative 41 answer. D X is equal to 13 and Y is equal to negative 28. So with the substitution method, we need to solve one of our equations for X and Y as the first step. So looking at our second equation, we see that we can easily solve for X by first just subtracting three Y from both sides of the equation, we have negative X is equal to negative minus three Y. Now we want X to be positive. So we can just multiply or divide both sides of the equation by negative one again to make X positive. And so we are left with the expression for X where X is equal to 154 plus three Y. So now we can just take this expression for X and substitute it in four X from our first equation. So instead of negative four, X is equal to two Y plus 98 we now have negative four times the quantity of 54 plus three Y and this is equal to two Y plus 98. So now we just want to factor in or distribute this negative four into the expression in the parentheses. And so we have negative 616 minus 12, Y is equal to two Y plus 98. So now we just want to get our Y two terms to be on the same side of the equation. So we can just add 12 Y to both sides. So we have negative 616 is equal to 14, Y plus 98. Now we need to get Y alone. So we, we first need to subtract 98 from both sides. And so we have negative 714 is equal to 14. Y. Now continuing to get Y alone, we need to divide by its coefficient which is 14. So we divide both sides of the equation by 14 and we get Y is equal to negative 51. And so now with this value for Y, we can substitute it into our expression that we found for X. So instead of X is equal to 154 plus three, Y, we now have X is equal to plus three times the value of Y, which we found to be negative 51. Now just simplifying the product, we have X is equal to 154 plus three times negative 51 which gives us negative 153. Now, just combining these terms, we have X is equal to one. And so we have found our value for X and our value for Y. And so we are left with answer choice B where X is equal to one and Y is equal to negative 51. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Solve each system by substitution.
-2x = 6y + 18
-29 = 5y - 3x

Key Concepts

System of Linear Equations

Substitution Method

Algebraic Manipulation

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