7x + 2y = 24 8x + 2y = 30

Subtract first equation from the second.

what does that mean

To solve this system of equations, we can use the method of substitution or the method of elimination. I will explain both methods and then show you how to solve the given system of equations using the method of elimination.

Method of Substitution:
1. Choose one of the equations and solve it for one variable in terms of the other variable. Let's solve the first equation for x.
7x + 2y = 24
Subtract 2y from both sides:
7x = 24 - 2y
Divide both sides by 7:
x = (24 - 2y) / 7

2. Substitute the expression you found for x into the other equation. Let's substitute it into the second equation.
8x + 2y = 30
Replace x with (24 - 2y) / 7:
8((24 - 2y) / 7) + 2y = 30
Simplify and solve for y.

3. Once you find the value of y, substitute it back into one of the original equations to solve for x.

Method of Elimination:
1. Multiply both sides of the first equation by 4 and the second equation by -3 to make the coefficients of y in both equations equal:
28x + 8y = 96
-24x - 6y = -90

2. Add the two equations together to eliminate the y term:
(28x - 24x) + (8y - 6y) = 96 - 90
4x + 2y = 6

3. Solve this single equation for one variable in terms of the other variable. Let's solve it for x:
4x = 6 - 2y
Divide both sides by 4:
x = (6 - 2y) / 4

4. Substitute the expression you found for x into one of the original equations to solve for y.

Now let's solve the given system of equations using the method of elimination:

1. Multiply both sides of the first equation by 4 and the second equation by -3:
28x + 8y = 96
-24x - 6y = -90

2. Add the two equations together:
(28x - 24x) + (8y - 6y) = 96 - 90
4x + 2y = 6

3. Solve this equation for one variable in terms of the other variable. Let's solve for x:
4x = 6 - 2y
Divide both sides by 4:
x = (6 - 2y) / 4

4. Now substitute this expression for x into one of the original equations. Let's use the first equation:
7x + 2y = 24
Replace x with (6 - 2y) / 4:
7((6 - 2y) / 4) + 2y = 24

5. Simplify and solve for y. Once you find the value of y, substitute it back into one of the original equations to solve for x.