Question

5x+y=9 10x-7y=-18

Answer 1

are u solving for both x and y?

Answer 2

If you are solving for both x and y, then there are 2 options that you can choose. One is using the substitution method and the other one is using the elimination method. First I will show you the substitution method because it will be easier to use this method when solving this problem. But I will also show you the elimination method.

Substitution Method:
1.) Solve for y in the first equation: \[y=-5x+9\]
2.) Plug in the y value in the second equation: \[10x-7(-5x+9)=-18\]
3.) Distribute: \[10x+35x-63=-18\]
4.) Add like terms: \[45x-63=-18\]
5.) Solve for x: \[45x=45\]
\[x=1\]
6.) Now that you have the x value, plug in this x value to any of the 2 equations above. I'm going to plug in to the first equation because it's easier: \[5(1)+y=9\]
7.) Solve for y: \[5+y=9\]
\[y=4\]
Therefore, your answer is x=1 and y=4
Sometimes, for tougher equations, it is easier to use the elimination method instead of the substitution method. I will show you this now.

Elimination Method:
1.) Set the equation so that same variables will be in the same column:
\[5x+y=9\]
\[10x-7y=-18\]
2.) Multiply the top equation by 2 (you are doing this to cancel out one of the variables. In this case, it will be easier to cancel out x because you can multiply by a small number)

3.) \[10x+2y=18\]
\[10x-7y=-18\]

4.) Subtract the top equation by the bottom equation:
\[10x+2y=18\]-\[(10x-7y=-18)\]

5.) You will get
\[9y=36\]

6.) Solve for y
\[y=4\]

7.) Now that you have the y value, plug in to one of the two equations above. I will plug in to the first equation because it is easier to do so.
\[5x+(4)=9\]

8.) Solve for x
\[5x=5\]
\[x=1\]

9.) So your answer is x=1 and y=4.

Whichever method you choose, you will get the same answer but one method will work better than the other one in different equations.

I really hope this helped :D