Question

Solve the system of equation by ELIMINATION: -2x - y = -9 5x - 2y = 18

Answer 1

x = 4

y = 1

Step-by-step explanation:

The system of equation is:

-2x - y = -9

5x - 2y = 18​

To solve the system by elimination, we will multiply the first equation by -2, so:

`\begin{gathered} -2x-y=-9 \\ -2(-2x-y)=-2(-9) \\ -2(-2x)-2(-y)=-2(-9) \\ 4x+2y=18 \end{gathered}`

Now, we can add this equation to the second equation:

4x + 2y = 18

5x - 2y = 18

9x + 0 = 36

So, solving the equation, we get:

9x = 36

9x/9 = 36/9

x = 4

Finally, we replace the value of x on the first equation:

4x + 2y = 18

4(4) + 2y = 18

16 + 2y = 18

Solve for y:

16 + 2y - 16 = 18 - 16

2y = 2

2y/2 = 2/2

y = 1

Therefore, the solution of the system is x = 4 and y = 1.