Question

Alvin’s first step in solving the given system of equations is to multiply the first equation by 2 and the second equation by –3. Which linear combination of Alvin’s system of equations reveals the number of solutions to the system?

9x + 4y = 36

6x + 2.5y = 24

Answer 1

solving we get Solution set = {4,0}

Explanation:

We are given system of equation:

`9x + 4y = 36---eq(1)\\6x + 2.5y = 24---eq(2)`

Multiply eq(1) by 2 and eq(2) by -3

`18x \ \ + 8y \ \ \ = 72\\-18x - 7.5y = -72\\---------\\0.5y=0\\y=0`

We get y=0,

Now finding x by putting value of y in eq(1)

`9x + 4y = 36\\9x+4(o)=36\\9x=36\\x=(36)/(9)\\x=4`

So, solving we get Solution set = {4,0}