Question

HELP PLEASE !!! Aneesha used linear combination to solve the system of equations shown. She did so by multiplying the first equation by 5 and the second equation by another number to eliminate the y-terms. What number did Aneesha multiply the second equation by?
1. 6x + 2y = 28
7 x - 5y = - 4

Clare used linear combination to solve the system of equations shown. She did so by multiplying the second equation by a certain number to eliminate the x-terms. What number did Clare multiply the second equation by?
x - y = 5
0.5x + 0.1y = 8.5

Answer 1

1.
Multiply each equation by the value that makes the coefficients of y opposite.

5*(6x+2y)=5(28) 
2*(7x−5y)=2(−4)

Simplify

30x+10y=140 
14x−10y=−8

Add the two equations together to eliminate y from the system.

44x = 132
Simplify the equation and solve for x.

x = 3
Substitute the value found for x into one of the original equations, then solve for y.
y=5

(3,5)

Multiplied second equation by 2.

2.
x - y = 5
0.5x + 0.1y = 8.5

Multiply each term in the equation by 10.
10x−10y=50 
5x+y=85

Multiply each equation by the value that makes the coefficients of x opposite.
−1*(10x−10y)=−1(50) 
2*(5x+y)=2(85)

Simplify

−10x+10y=−50 
10x+2y=170

Add the two equations together to eliminate x from the system.
12y = 120

Simplify the equation and solve for y.
y=10

Substitute the value found for y into one of the original equations, then solve for x.
x=15

(15,10)

Multiplied the second equation by 2.

Answer 2

In problem number 1, the answer is 2. because if Aneesha multiply the first equation with 5, 2y will become 10y and if she multiply the sencond equation with 2, 5y will become 10y and 10y from both equations cancel out each other.

in problem number 2, the answer is 2. it's the same logic as number 1. if you multiply 0.5x with 2, it will become 1 and cancel out with x from first equation.