Question

What value does each equation need to be multiplied by in order to eliminate the y-terms?

Equation 1: 6x − 5y = -4
Equation 2: 4x + 2y = 28

Please Help, I don't get it

Answer 1

Equation 1 needs to be multiplied with + 2

Equation 2 needs to be multiplied with + 5.

Explanation:

Here, the given system of equation is given as:

Equation 1 : 6 x − 5 y = -4

Equation 2: 4 x + 2 y = 28

Here, in equation 1, the coefficient of y = - 5

Also, in the equation 2, the coefficient of y = + 2

Now, in order to eliminate the y coefficients,

Coefficient of y in 1 = - Coefficient of y in 2

Now, to make -5 and + 2 to eliminate each other,

Multiply -5 with 2, we get -5 x 2 = -10

And Multiply the coefficient + 2 with 5, we get +2 x 5 = + 10

The new coefficient of y is equation 1 = - 10 y

The new coefficient of y in equation 2 = + 10 y

They will cancel out each other, when both equations are ADDED.

Hence, equation 1 needs to be multiplied with + 2

and the equation 2 needs to be multiplied with + 5.