Question

What is the y-coordinate for the solution to the system of equations?

{6x + 11y = −3
{4x + y = 17
Enter your answer as the correct value, like this: 42

Answer 1

Answer:

-3

Step-by-step explanation:

6x + 11y = -3

4x + y = 17

1. Since you want to find y, you should "get rid" of the x. To do this, find the LCD of the coefficients of x and find what number gets those coefficients to the LCD. Then remember that when you multiply each equation by their number, make one of those negative so that it "cancels out". If this is confusing my work will explain

6x + 11y = -3

4x + y = 17

2. List out multiples of 6 and 4:

6: 6, 12,18,24

4: 4,8,12,16

12 is their LCD

3. To get to 12, 4 has to be multiplied by 3, and 6 has to be multiplied by 3

I'm choosing to multiply 4 by -3, otherwise, 6 would have been multiplied by -3. Then distribute

2(6x + 11y = -3) => 12x + 22y = -6

-3(4x + y = 17) => -12x - 3y = -51

4. Add terms

$\left \{ {{12x + 22 y =-6} \atop {-12x-3y=-51} \right.$  22y - 3y = 19y and -6 (+) -51 = -6-51 = -57

19y = -57

5. Divide

y = -57/19 = -3

y = -3

Answer 2

Answer:

y = -3

Step-by-step explanation:

$\left\{\begin{array}{ccc}6x+11y=-3&\text{multiply both sides by 2}\\4x+y=17&\text{multiply both sides by (-3)}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}12x+22y=-6\\-12x-3y=-51\end{array}\right}\qquad|\text{add all sides of the equations}\\.\qquad19y=-57\qquad|\text{divide both sides by 19}\\.\qquad y=-3$