Question

Can someone please help!!!

Answer 1

Answers:

• System 1:  x = 3 and y = -5
• System 2: x = 1 and y = 2

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Explanation:

For now, let's focus on system 1.

We have identical copies of "2y" in each equation, which means that if we were to subtract the equations straight down, then the y terms cancel out. That allows us to solve for x.

• The x terms subtract to 7x-x = 6x
• The y terms subtract to 0 and go away
• The right hand sides subtract to 11 minus (-7) = 11-(-7) = 11+7 = 18

After doing those subtractions, we have the new equation 6x = 18 which solves to x = 3. Divide both sides by 6 to isolate x.

Once we know x, we can find out y.

7x+2y = 11

7(3)+2y = 11

21+2y = 11

2y = 11-21

2y = -10

y = -10/2

y = -5

or we can say

x+2y = -7

3+2y = -7

2y = -7-3

2y = -10

y = -10/2

y = -5

We should lead to the same y value either way. This helps confirm we have the correct x value.

Overall, the solution to system 1 is (x,y) = (3, -5)

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Now onto system 2.

Unfortunately, we don't have identical y terms this time. But what we can do is double everything in the second equation to go from -x+y = 1 to -2x+2y = 2.

The new equivalent system is

$\begin{cases}7x+2y = 11\\-2x+2y = 2\end{cases}$

Now we have the same situation as before: Subtract straight down, solve for x.

• The x terms subtract to 7x-(-2x) = 7x+2x = 9x
• The y terms go away when subtracting
• The right hand sides subtract to 11-2 = 9

So we have 9x = 9 and that solves to x = 1.

We'll use this x to find the y value.

7x+2y = 11

7(1)+2y = 11

7+2y = 11

2y = 11-7

2y = 4

y = 4/2

y = 2

Or you could pick on the second equation

-x+y = 1

-1+y = 1

y = 1+1

y = 2