Question

Solve each system of equations by writing a new system that eliminates one of the variables.

Answer 1

Answer:

$x=33\\y=-41$

Step-by-step explanation:

Let:

$2x+y=25\hspace{5}(1)\\and\\4x+3y=9\hspace{5}(2)$

We need to eliminate one of the variables, so let's use elimination method. First multiply (1) by 2

$2*(1)\equiv\hspace{5}4x+2y=50$

Now subtract (2) from 2*(1) in order to eliminate x:

$2*(1)-(2)\\4x-4x+2y-3y=50-9\\-y=41$

Solving for y:

Multiplying both sides by -1  

$y=-41$

Finally, replacing the value of y in (1)

$2x-41=25$

Solving for x:

add 41 to both sides:

$2x=66$

Multiply both sides by 1/2:

$x=\frac{66}{2} =33$