solve the system

Question

2x+3y=9

x-2y=8

Solve for x and y for the following two equations please.And please do step by step so i can get a better understanding.

Answer 1

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Answer 2

Start with the second equation and solve for x:

x = 2y+8

Now substitute for x in the first equation:

2(2y+8) + 3y = 9

Solve for y:

4y+16 + 3y = 9

7y = 9-16 = -7

y = -7/7 = -1

Use this value to solve for x

x=2y+8= 2(-1)+8 = -2+8 =6

x = 6

y = -1

Answer 3

Hello Olivia,

You want to solve this system of equations:

2x+3y=9 Equation #1

x-2y=8 Equation #2

Let's use elimination. You can multiply the 2nd equation by -2. That will allow you to eliminate the x variable when adding the 2 equations.

Multiplying the 2nd equation by -2 gives you the following system:

2x + 3y =9 [ this equation is unchanged]

-2x +4y=-16 [ we multiplied 1 by -2 to get the new x coefficient, -2 by -2 to get the new y coefficient, 8 by -2 to get the new constant]

Now you can add both equations. You get:

2x + - 2x + 3y + 4y = 9 + -16

You can see the 2x and the -2x will cancel each other out, so you now have:

7y = -7

Divide both sides by 7 and you get y = -1

Now insert that y value into any of the 2 equations of your system. Let's do the 2nd one

x - 2(-1) = 8 -----> x + 2 = 8

subtract 2 from each side ------> x = 6

Let's do a final check to make sure the x and y we found are solutions for the system:

Equation #1: does 2(6) + 3(-1) equal 9? 12 + (-3) = 9 so yes.

Equation #2: does 6 - 2(-1) equal 8? 6 +2 = 8 so yes

Check successful, so the solution is x = 6, y = -1.