Question

question 6
a system of two equations is to be solved by elimination.
equation a: $2x + 5y = 15$
equation b: $10y = -4x + 30$
what is true about the equations? select all that apply.

• equation b can be rewritten as $4x + 10y = 30$.
• equation b can be rewritten as $10y - 4x = 30$.
• the two equations are equivalent, so there is an infinite number of solutions.
• if you multiply equation a by negative two, then it is $4x + 10y = 30$.
• the two equations are parallel lines, so there is no solution.
• if you multiply equation a by two, then it is $4x + 10y = 30$

question 7

Explanation:

Step1: Rearrange Equation B

Start with $10y = -4x + 30$. Add $4x$ to both sides:
$4x + 10y = 30$
This confirms option A is correct, option B is incorrect.

Step2: Scale Equation A

Multiply Equation A ($2x + 5y = 15$) by 2:
$2*(2x + 5y) = 2*15$
$4x + 10y = 30$
This confirms option F is correct, option D is incorrect.

Step3: Compare equations

Equation B rearranged equals the scaled Equation A, so they are equivalent. Equivalent linear equations have infinitely many solutions, so option C is correct, option E is incorrect.

Answer:

A. Equation B can be rewritten as $4x + 10y = 30$.
C. The two equations are equivalent, so there is an infinite number of solutions.
F. If you multiply Equation A by two, then it is $4x + 10y = 30$.