Question

Solve the system of equations using the linear combination method. 3x-2y=13 4x+5y=2

Answer 1

Answer:

The solution of the system will be:  $x= 3$ and $y=-2$

Step-by-step explanation:

The given system of equations is.......

$3x-2y=13................................(1)\\ \\ 4x+5y=2..................................(2)$

Multiplying equation (1) by 5 and equation (2) by 2, we will get........

$5(3x-2y)=5(13)\\ 15x-10y=65...............................(3)\\ \\ and\\ \\ 2(4x+5y)=2(2)\\ 8x+10y=4...................................(4)$

Now, adding equation (3) and (4), we will get.........

$(15x-10y)+(8x+10y)=65+4\\ \\ 23x=69\\ \\ x=\frac{69}{23}=3$

Plugging this $x=3$ into equation (1).........

$3(3)-2y=13\\ \\ 9-2y=13 \\ \\ -2y=4\\ \\ y=\frac{4}{-2}=-2$

So, the solution of the system will be:  $x= 3$ and $y=-2$