Question

Pls I need help this assignment is done before 11:59pm.

Solving systems of equations using substitution.

Can you also explain cause I didn’t understood that much.

Thanks.

Answer 1

Answers:

• Blank 1 = 3
• Blank 2 = 3

In other words, x = 3 and y = 3

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Step-by-step explanation:

Let's solve the first equation for x. I'm picking on this equation variable because the coefficient is 1.

Solving for x leads to

x-2y = -3

x = -3+2y

I added 2y to both sides

Now we'll plug this into the other equation. This means we replace every copy of x with -3+2y since they are the same thing.

3x + 5y = 24

3( x ) + 5y = 24

3( -3+2y ) + 5y = 24 .... replace x with -3+2y

3(-3) + 3(2y) + 5y = 24 .... distribute

-9 + 6y + 5y = 24

11y-9 = 24

11y-9+9 = 24+9 ...... adding 9 to both sides

11y = 33

11y/11 = 33/11 .... dividing both sides by 11

y = 3

We'll use this y value to find x. We can pick on any equation with x & y in it, but I find it's easiest to use the equation where x is isolated

x = -3+2y

x = -3+2(3) .... replace y with 3

x = -3+6

x = 3

So both x and y are equal to 3

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Let's check the answer

Plug (x,y) = (3,3) into the first equation. We should get the same number on both sides after simplifying fully

x-2y = -3

3 - 2(3) = -3

3 - 6 = -3

-3 = -3

So far, so good. Let's try the other equation

3x + 5y = 24

3(3) + 5(3) = 24

9 + 15 = 24

24 = 24

The other equation is true as well. This fully confirms that (x,y) = (3,3) is the solution to this system of equations. If you graphed each original equation, you should find they cross at the location (3,3).

Side note: it won't always be the case that x and y are the same value.