Solve each system by substitution.
8x - 10y = -22

Question

Solve each system by substitution.

8x - 10y = -22

3x + y = 6

Accepted Answer

Hey, everyone here we are asked to use the substitution method to solve the following system of equations where the first equation is three, X minus five, Y is equal to negative two. And the second given equation is four, X plus two, Y is equal to six. Here we have four answer choice options. Answer a no solution. Answer B X is equal to zero and Y is equal to zero. Answer C X is equal to one and Y is equal to one and answer D X is equal to five and Y is equal to five. So here to use the substitution method, we need to select either the first or second equation and solve for either X or Y. Here, I'm going to choose the second equation and solve for Y. So solving for Y, we first just subtract four X from both sides of the equation. So we have two, Y is equal to six minus four X. Now to finish solving four, Y, we just divide both sides of the equation by its coefficient which is two. So we have Y is equal to three minus two X. So now using this expression, we found four Y, we need to substitute it into our first given equation so that we can solve for X. So originally our first equation is three, X minus five Y is equal to negative two. And now substituting in our expression, we have three X minus five times the quantity of three minus two, X is equal to negative two. And so now we just want to distribute in negative five into our expression in the parentheses. So we have three X minus 15 plus 10, X is equal to negative two. Now just combining like terms, we have 13, X minus 15 is equal to negative two. And now just solving for X, we first add 15 to both sides of the equation. And so we have 13 X is equal to 13. Now dividing both sides by the coefficient of X, we divide both sides by 13 and we find our value for X is just one. So now with this value of X, we can go back to our equation. We found of Y where Y is equal to three minus two X and now we can just substitute in this value. We found four X. So we now have Y is equal to three minus two times our value that we found for X, which is one. Now simplifying the product we have Y is equal to three minus two. And now simplifying further, we see Y is simply equal to one as well. So here, we have found our value for X and Y and so we are left with answer choice C where X is equal to one and Y is equal to one as well. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Solve each system by substitution.
8x - 10y = -22
3x + y = 6

Key Concepts

System of Linear Equations

Substitution Method

Solving Linear Equations

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