Question

Slove the equation for y and x
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Answer 1

Answer: y = -2x + 1

Solution to the system: (2,-3)

Explanation:

2x + y = 1

3x + 2y = 0

We can solve this using substitution

The first thing that we're going to want to do is solve for y in the first equation

Solve for y

2x + y = 1

Subtract 2x from both sides

y = 1 - 2x

We now have the two equations

y = -2x + 1 and 3x + 2y = 0

The next step in solving the system is to plug in the expression of y ( -2x + 1) into the second equation

3x + 2y = 0

Substitute -2x + 1 for y

3x + 2(-2x + 1) = 0

Now solve for x

Distribute the 2 to the -2x and 1

2 * -2x = -4x

2 * 1 = 2

We now have 3x - 4x + 2 = 0

Combine like terms

-x + 2 = 0

Add x to both sides

2 = x

Now to find the value of y we substitute the value of x into one of the equations and solve for y

2x + y = 1

x = 2

2(2) + y = 1

Multiply

4 + y = 1

Subtract 4 from both sides

y = -3

The solution to the system is (2,-3)

And we are done!

Answer 2

x=2

y=-3

Explanation:

2x+y = 1

3x+2y = 0

Multiply the first equation by -2

-4x-2y = -2

Add this to the second equation

-4x-2y = -2

3x+2y = 0

-------------------

-x = -2

Multiply by -1

x = 2

Now find y

2x+y = 1

2(2) +y = 1

4 +y = 1

Subtract 4 from each side

y = 1-4

y = -3