Solving this System of Equations

Question

These are the equations:

10y+7x=29

−5y−9x=2​

The question is asking me to solve the system of questions to find X & Y.

I just cannot understand how to solve these. Please help! Thank you!

Answer 1

Question: Solve for x and y:

10y+7x=29

−5y−9x=2​

Solution: Part of the battle with solving systems of equations is knowing which method to use, and while you technically could use any method like graphing, substitution, or elimination, the structure of this system lends itself well to elimination and is more easily done by elimination.

Do you see how the x-terms and y-terms and constants are already lined up nicely for you? Also, do you see in the y-column that 10 is a multiple of 5? (Think: 5, 10, 15, 20, etc.) These are good indications that you could rewrite the bottom equation to make the y-terms cancel out. Let me explain:

-5y • 2 = -10y. The top equation has positive 10y. When you add up the equations, 10y + (-10y) = 0y = 0, so those terms cancel out. However, the entire bottom equation needs to be multiplied by 2; you can't just single out one term for this treatment.

Here is what we have so far:

10y+7x=29

−5y−9x=2​

10y+7x=29

2(−5y−9x=2​)

10y+7x=29

−10y−18x=4

Add the equations together:

-11x = 33

Solve as normal by division:

x = -3.

That's the hardest part, I think, is to solve for the first variable, either x or y. Now you take this fact that x = -3 and plug it into either of the original equations; it doesn't which one you pick. Plug it in and solve for y. I'll pick the first equation:

10y+7x=29

10y+7(-3)=29

10y - 21 = 29

10y = 50

y = 5.

So x = -3 and y = 5. Or put another way, the solution to this system of equations is (-3, 5).

I hope this helps!

Answer 2

multiply 1st equation by 5

then multiply 2nd by 10

then add to get -55x = 165

x = 165/-55 = -3

y = 5

x=-3, y = 5

Answer 3

1) 10y+7x=29

2) −5y−9x=2​

3) -10y - 18x = 4, multiply both sides of 2) by 2

4) -11x = 33, add 3) to 1)

5) x = -3, divide both sides of 4) by -11

Can you substitute x = -3 in either 1) or 2) and determine y?