Solve: 3x-2y=10 2x+3y=-2

Graph:
Substitution:
Elimination:

Show Your work!
(I can'tfigure out how to graph it and when i used substitution and elimination it came out with two different anwsers. I got (13/3.5,19/10.5) for substitution, and ((0.2,-0.8) for Elimination.I need help, and i need to be able to show my work!)

3x-2y=10 2x+3y=-2

By substitution
3x - 2y = 10
2x + 3y = -2

3x = 10 + 2y
x = 10/3 + 2/3 y

2(10/3 + 2/3 y) + 3y = -2
20/3 + 4/3 y + 3y = -2
20/3 + 4/3 y + 9/3 y = -2
20/3 + 13/3 y = -2
13/3 y = -2 - 20/3
13/3 y = -6/3 - 20/3
13/3 y = - 26/3
y = -26/3 * 3/13
y = - 78/39 = -2

to find x, sub y = -2 in,
2x + 3y = -2
2x - 6 = -2
2x = 4
x = 2

So, x = 2, y = -2

By elimination
3x - 2y = 10
2x + 3y = -2

Multiply 3 (3x - 2y = 10)
9x - 6y = 30
Multiply 2 (2x + 3y = -2)
4x + 6y = -4

9x - 6y = 30
4x + 6y = -4
13x = 26
x = 2

to find y, sub x = 2 in,
2x + 3y = -2
4 + 3y = -2
3y = -6
y = -2

To solve the given system of linear equations, we will go step by step through the three methods: graphing, substitution, and elimination.

1. Graphing:
To graph the system, we need to plot the points that satisfy both equations on a coordinate plane.

Equation 1: 3x - 2y = 10
To graph this equation, we can rearrange it to solve for y:
-2y = -3x + 10
y = (3/2)x - 5

Equation 2: 2x + 3y = -2
To graph this equation, we can rearrange it to solve for y:
3y = -2x - 2
y = (-2/3)x - (2/3)

Now, we can plot the two equations on the coordinate plane:

{{{ graph( 300, 200, -5, 5, -10, 10, (3/2)*x - 5, (-2/3)*x - (2/3) ) }}}

The solution to the system is the point where the two lines intersect, which appears to be approximately (0.2, -0.8).

2. Substitution:
Let's use the substitution method to solve the system:

From Equation 1, we can solve for x:
3x - 2y = 10
3x = 2y + 10
x = (2/3)y + (10/3)

Now, substitute this expression for x in Equation 2:
2((2/3)y + (10/3)) + 3y = -2
(4/3)y + (20/3) + 3y = -2
(13/3)y = -26/3
y = -26/3 * (3/13)
y = -2

Substitute this value of y back into Equation 1 to find x:
3x - 2(-2) = 10
3x + 4 = 10
3x = 6
x = 2

Therefore, the solution to the system using substitution is (2, -2).

3. Elimination:
Let's use the elimination method to solve the system:

Multiply Equation 1 by 2 and Equation 2 by 3 to eliminate the y-term:
6x - 4y = 20
6x + 9y = -6

Now, subtract Equation 1 from Equation 2:
(6x + 9y) - (6x - 4y) = -6 - 20
13y = -26
y = -26/13
y = -2

Substitute this value of y back into Equation 1 to find x:
3x - 2(-2) = 10
3x + 4 = 10
3x = 6
x = 2

Therefore, the solution to the system using elimination is (2, -2).

So, for both the substitution and elimination methods, we found a consistent solution of (2, -2), which is different from the solution you mentioned. It's possible that there was an error in your calculations.