what is 7x-9y=13 and 9x+7y=91
elimination method
let's eliminate the y's
1st times 7 --> 49x -63y = 91
2nd times 9 -> 81x + 63y = 819
add them:
130x = 910
x = 7
back into 2nd ...
9(7) + 7y = 91
7y = 28
y = 4
x=7 , y = 4
The elimination method is a technique used to solve a system of linear equations. In this case, we have two equations:
1) 7x - 9y = 13
2) 9x + 7y = 91
To solve this system using the elimination method, we need to eliminate one of the variables by multiplying one or both equations by a suitable constant(s) so that when we add or subtract them, one variable cancels out.
In this case, let's eliminate the y variable. To do this, we will multiply equation 1) by 7 and equation 2) by 9, so that the coefficients of y are equal but opposite in sign. This will allow us to effectively eliminate y when we add the two equations:
Multiply equation 1) by 7:
7 * (7x - 9y) = 7 * 13
49x - 63y = 91
Multiply equation 2) by 9:
9 * (9x + 7y) = 9 * 91
81x + 63y = 819
Now, add the two equations together:
(49x - 63y) + (81x + 63y) = 91 + 819
49x + 81x - 63y + 63y = 910
Simplify:
130x = 910
To isolate x, divide both sides by 130:
130x / 130 = 910 / 130
x = 7
Now that we have found the value of x, we can substitute it back into either of the original equations to find the value of y. Let's sub it into equation 1):
7(7) - 9y = 13
49 - 9y = 13
Subtract 49 from both sides to isolate -9y:
-9y = 13 - 49
-9y = -36
Divide both sides by -9 to solve for y:
(-9y) / -9 = (-36) / -9
y = 4
Therefore, the solution to the system of equations is x = 7 and y = 4.