Question

#2: Solve the linear system below using the elimination method. Type your

answer as an ordered pair in the form (#,#). *
5x + 7y = 33
11x + 7y = 39
+

Answer 1

(1, 4)

Tbh this question was a bit of a challenge for me but hopefully it helps ya.

Explanation:

First, let's solve for y. So we have to eliminate the x values.

(5x + 7y = 33 ) *11

(11x + 7y = 39) *-5

___________

55x + 77y = 363

-55x -35y = -195 This eliminates the x value.

42y = 168 Divide both sides by 42 to isolate y: 168/42= y = 4

Now let's solve for x.

(11x + 7y = 39) *7

(5x + 7y = 33 ) *-7

___________

77x + 49y = 273

-35x -49y = -231 This cancels out the y values, which leaves 42x = 42

x = 1 and y = 4, so the answer is (1, 4)

Answer 2

The given linear system is:

`\displaystyle \left \{ {{5x+7y=33} \atop {11x+7y=39}} \right.`

The question is asking to solve using elimination. When eliminating, you can either eliminate x or y. In this system, y is much easier to eliminate. The y variable in both equations are 7y. To eliminate, one of them has to be negative, so multiply one of the equations by -1.

I will be multiplying the second equation by -1.

`\displaystyle (11x + 7y = 39) * -1 = -11x-7y=-39`

Rewrite the system:

`\displaystyle \left \{ {{5x+7y=33} \atop {-11x-7y=-39}} \right.`

Subtract:

`5x+7y=33\\-11x-7y=-39`

`5x-11x=33-39\\-6x=-6`

Lastly, you need to leave the variable x alone. The variable is currently -6x or -6 times x. To remove it, you need to do the opposite of it, which is dividing by -6.

`\displaystyle (-6x)/(-6) =(-6)/(-6)`

`\displaystyle x=1`

Now that you have the value of x, substitute it into one of the equations to find y. I will be substituting it into the first equation.

`5x+7y=33 \rightarrow 5(1)+7y=33`

Open the parentheses and multiply:

`5+7y=33`

Move 5 to the other side to leave the variable alone:

`5+7y-5=33-5`

You will be subtracting since you're "removing" it by doing the opposite of it.

`7y=28`

Lastly, divide both sides by 7 to leave y alone.

`\displaystyle (7y)/(7) =(28)/(7)`

`y=4`

`\displaystyle (x,y) \rightarrow (1, 4)`

The answer is (1, 4).