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write a system of linear equations in two variables that has a solution of (-4, 3). then demonstrate how to solve your system by elimination.

1 Answer

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Answer:

y - x = 7

y -2x = 11

Explanation:

y - x = 7

y - 2x = 11

Multiply the the first equation by -1 and then add the equations together

-y + x = -7

y -2x = 11

-x = 4 Multiply both sides by -1

x = -4

Substitute in -4 for x in either of the two original equations to solve for y

y - x = 7

y - (-4) = 7

y + 4 = 7 Subtract 4 from both sides

y = 3

The solution is the ordered pair (3,-4)

Here is how I came up with my equations. I know that I want y to be -4 and x to be 3.

y = mx + b If I select m to be 1, then I solve for b to write the equation

3 = (1)(-4) + b

3 = -4 + b Added 4 to both sides

7 = b

My equation is now:

y = (1)x + 7

or

y = x + 7

I changed the form by subtracting x from both sides so that it is friendly to use elimination to solve.

y - x = 7

For my second equation, I select 2 to be my m

y = mx + b

3 = (2)(-4) + b Solve for b

3 = -8 + b Add 8 to both sides

11 = b

y = mx + b

y = 2x + 11 and then subtracted 2x from both sides to make the equation friendlier to use elimination to solve.

y - 2x = 11

There is a lot going on here. I hope that it makes sense. If it doesn't make sense, it is me and not you.

Helping in the name of Jesus.

User Tbert
by
7.3k points

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