Question

Solve the system by substitution and show all steps.

Answer 1

Answer:

(-1, -4)

Step-by-step explanation:

We have the following system of equations:

$-4.5x-2y=12.5\\3.25x-y=0.75$

We can solve this using substitution.

First, from the second equation, let's subtract 3.25x from both sides. So:

$-y=0.75-3.25x$

We can now substitute this into the first equation. Note that the first equation is the same as:

$-4.5x+2(-y)=12.5$

Substitute in -y. This yields:

$-4.5x+2(0.75-3.25x)=12.5$

Distribute:

$-4.5x+1.5-6.5x=12.5$

Combine like terms:

$-11x+1.5=12.5$

Subtract 1.5 from both sides:

$-11x=11$

Divide both sides by -11. So, the value of x is:

$x=-1$

To find y, we can use the equation we solved earlier:

$-y=0.75-3.25x$

Substitute -1 for x:

$-y=0.75-3.25(-1)$

Multiply:

$-y=0.75+3.25$

Add:

$-y=4$

Divide both sides by -1:

$y=-4$

So, our solution is (-1, -4).

And we're done!