Sustem of equations. I have to solve the system of equations by graphing and solving.

Ther are thirty-three students in the Chess Club. There are five more boys than girls in the club. Write and solve a system of equations to find the number of boys and girls in the chess club.

number of boys --- x

number of girls ---- y

x+y = 33

x-y = 5

add them:
2x = 38
x=19
then in the first:
x+y=33
19+y = 33
y = 33-19 = 14

We have 19 boys and 14 girls

check:
do we have 33 students ? yes
do we have 5 more boys than girls? YES!!!!

To graph this
first equation:
pick any two points so that x+y = 33
e.g. (15,18) and (5,28) , join them

2nd equation:
pick any two points so that x-y = 5
e.g.( 10,5) and (20,15) , join them

the two lines should intersect at (19,14)

Sure, let's solve this math problem using some humor!

Let's call the number of girls in the Chess Club "G" and the number of boys "B". Since we know that there are five more boys than girls, we can express this relationship with an equation:

B = G + 5

We also know that there are a total of 33 students in the Chess Club. So we can express this with another equation:

B + G = 33

Now let's see how these equations can help us find the number of boys and girls in the Chess Club.

Let's start by graphing these equations on a coordinate plane. But trust me, I promise, this circus is going to be worth it!

*Sets up a huge circus tent with a giant coordinate plane*

Now, let's bring out the performers: the boys and girls of the Chess Club!

*Thirty-three students dressed as chess pieces enter the circus tent*

Now, let's solve the system of equations by finding the point where these two equations intersect. Ah, yes, right under the circus spotlight!

*Shines a spotlight on the point where the two lines intersect*

And voila! The point of intersection represents the numbers of boys and girls.

Let's see... Ah, it looks like there are 19 boys and 14 girls in the Chess Club! So, if you want to check, just double-check your work using those numbers.

I hope this circus act helped you solve the system of equations and find the number of boys and girls in the Chess Club! If you have any more math questions, feel free to ask. Enjoy the show!

Let's assume the number of girls in the Chess Club is "x."

According to the given information, there are five more boys than girls in the club. Therefore, the number of boys in the Chess Club is "x + 5."

We also know that the total number of students in the Chess Club is thirty-three. So the equation representing the total number of students is:

x + (x + 5) = 33

Now we can solve this equation step-by-step:

1. Combine like terms: 2x + 5 = 33
2. Subtract 5 from both sides: 2x = 28
3. Divide by 2: x = 14

So, there are 14 girls in the Chess Club. To find the number of boys, we substitute the value of x back into our equation:

Number of boys = x + 5 = 14 + 5 = 19

Therefore, there are 14 girls and 19 boys in the Chess Club.

To solve this system of equations by graphing, you need two separate equations that represent the given information.

Let's assign a variable to the number of girls in the chess club. Since there are five more boys than girls, the number of boys can be represented as (number of girls + 5).

Now we can form the equations:
1) Number of girls: G
2) Number of boys: B = G + 5

To solve for G and B, we can substitute the value of B from the second equation into the first equation:

1) G + (G + 5) = 33

Combine like terms:
2G + 5 = 33

Subtract 5 from both sides:
2G = 28

Divide both sides by 2 to isolate G:
G = 14

Now we know that there are 14 girls in the chess club. To find the number of boys, substitute the value of G into the second equation:

B = 14 + 5
B = 19

Therefore, the number of boys in the chess club is 19.

To graph this system of equations, plot the number of girls (G) on the x-axis and the number of boys (B) on the y-axis. Draw the graph for each equation and find the point where the two lines intersect. In this case, the intersection point should be (14, 19), representing 14 girls and 19 boys in the chess club.