Question

Solving with Elimination Practice%0D%0AComplete this assessment to review what you've learned. It will not count toward your grade.%0D%0A2 of 52 of 5 Items%0D%0A%0D%0A%0D%0A%0D%0AQuestion%0D%0ASolve the system of equations.%0D%0A2x+8y=8%0D%0A2%0D%0A%0D%0A+%0D%0A8%0D%0A%0D%0A=%0D%0A8%0D%0A%0D%0A2x−4y=−16%0D%0A2%0D%0A%0D%0A−%0D%0A4%0D%0A%0D%0A=%0D%0A−%0D%0A16%0D%0A(1 point)%0D%0A(, )

Answer 1

To solve the system of equations, we can use the method of elimination.

First, let's multiply the second equation by 4 to make the coefficients of y match in both equations:

2x + 8y = 8
2x - 4y = -16

After multiplying the second equation by 4, we get:

2x + 8y = 8
8x - 16y = -64

Now, we can subtract the first equation from the second equation:

(8x - 16y) - (2x + 8y) = -64 - 8
6x - 24y = -72

Simplifying, we get:

6x - 24y = -72

Now, let's multiply the second equation by 3 to make the coefficients of x match in both equations:

2x + 8y = 8
6x - 24y = -72

After multiplying the second equation by 3, we get:

2x + 8y = 8
18x - 72y = -216

Now, we can subtract the first equation from the second equation:

(18x - 72y) - (2x + 8y) = -216 - 8
16x - 80y = -224

Simplifying, we get:

16x - 80y = -224

Now, we have the following system of equations:

6x - 24y = -72
16x - 80y = -224

To eliminate y, we can multiply the first equation by 5 and the second equation by -2:

(6x - 24y)(5) = (-72)(5)
(16x - 80y)(-2) = (-224)(-2)

30x - 120y = -360
-32x + 160y = 448

Now, we can add the two equations:

(30x - 120y) + (-32x + 160y) = (-360) + 448
-2x + 40y = 88

Simplifying, we get:

-2x + 40y = 88

Now, let's multiply this equation by -4 to eliminate y:

(-2x + 40y)(-4) = (88)(-4)
8x - 160y = -352

Now, we can add this equation to the equation 16x - 80y = -224:

(8x - 160y) + (16x - 80y) = (-352) + (-224)
24x - 240y = -576

Simplifying, we get:

24x - 240y = -576

Now, let's multiply this equation by 5 to eliminate x:

(24x - 240y)(5) = (-576)(5)
120x - 1200y = -2880

Now, we can add this equation to the equation -2x + 40y = 88:

(120x - 1200y) + (-2x + 40y) = (-2880) + 88
118x - 1160y = -2792

Simplifying, we get:

118x - 1160y = -2792

Now, we have the following system of equations:

-2x + 40y = 88
118x - 1160y = -2792

To eliminate y, we can multiply the first equation by 29 and the second equation by -1:

(-2x + 40y)(29) = (88)(29)
(118x - 1160y)(-1) = (-2792)(-1)

-58x + 1160y = 2552
-118x + 1160y = 2792

Now, we can add the two equations:

(-58x + 1160y) + (-118x + 1160y) = 2552 + 2792
-176x + 2320y = 5344

Simplifying, we get:

-176x + 2320y = 5344

Now, we have the following system of equations:

-176x + 2320y = 5344
118x - 1160y = -2792

To eliminate x, we can multiply the first equation by 118 and the second equation by 176:

(-176x + 2320y)(118) = (5344)(118)
(118x - 1160y)(176) = (-2792)(176)

-20768x + 273760y = 630272
20768x - 204160y = -491392

Now, we can add the two equations:

(-20768x + 273760y) + (20768x - 204160y) = 630272 + (-491392)
692600y = 138880

Simplifying, we get:

692600y = 138880

Dividing both sides by 692600, we find:

y = 0.2

Now, substitute this value of y into one of the original equations:

2x + 8(0.2) = 8
2x + 1.6 = 8
2x = 6.4
x = 3.2

Therefore, the solution to the system of equations is (x, y) = (3.2, 0.2)