Question

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

Answer 1

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.

$\displaystyle (11x + 7y = 39) \times -1 = -11x-7y=-39$

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.

$\displaystyle \frac{-6x}{-6} =\frac{-6}{-6}$

$\displaystyle x=1$

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.

$\displaystyle \frac{7y}{7} =\frac{28}{7}$

$y=4$

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

The answer is (1, 4).

Answer 2

Answer:

(1, 4)

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

Step-by-step 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)