Question

Suppose 3x + 4y = 52 and 5x + y = 30. What is the value of 8x − 2y?

A) 6
B) 8
C) 12
D) 32

Answer 1

interesting

just solve them to find x and y

3x+4y=52

5x+y=30

eliminate

eliminate y

multiply 2nd equation by -4

-20x-4y=-120

add to other equation

3x+4y=52

-20x-4y=-120 +

-17x+0y=-68

-17x=-68

divide both sides by -17

x=4

subsitute back

3x+4y=52

3(4)+4y=52

12+4y=52

minus 12 both sides

4y=40

divide both sides by 4

y=10

x=4 and y=10

subsitute

8x-2y=8(4)-2(10)=32-20=12

answer is 12

C is answer

Answer 2

`\left\{\begin{array}{ccc}3x+4y=52\\5x+y=30&|\cdot(-4)\end{array}\right\\\underline{+\left\{\begin{array}{ccc}3x+4y=52\\-20x-4y=-120\end{array}\right}\ \ \ \ \ |add\ both\ sides\\.\ \ \ \ \ -17x=-68\ \ \ \ \ |:(-17)\\.\ \ \ \ \ \ \ \ \ \ \ \ x=4\\\\put\ the\ value\ of\ x\ to\ the\ second\ equation\\\\5(4)+y=30\\20+y=30\ \ \ \ |-20\\y=10\\\\8x-2y=8(4)-2(10)=32-20=12\\\\Answer:\ \boxed{C)\ 12}`