Question 1199812
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Let's say we wanted to eliminate the variable y.


The y terms from the 1st and 2nd equations are -7y and -8y respectively.


The coefficients -7 and -8 do not add to zero. To fix this, we can multiply both sides of the first equation by 8 and the second equation by -7


8x-7y = -6 becomes 64x-56y = -48
7x-8y = -9 becomes -49x+56y = 63


At this point the y terms are -56y and 56y. They add to 0y or simply 0. The y variables are eliminated.


Add the x terms: 64x+(-49x) = 15x
Add the right hand side constants: -48+63 = 15


We arrive at 15x = 15 which solves to x = 1.


Once we determine x, use it to find the value of y.
8x-7y = -6
8*1-7y = -6
8-7y = -6
-7y = -6-8
-7y = -14
y = -14/(-7)
y = 2


<font color=red>The solution is (x,y) = (1,2)</font>


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Check:


Plug x = 1 and y = 2 into the first original equation
8x-7y = -6
8*1-7*2 = -6
8-14 = -6
-6 = -6
That equation is confirmed.


Repeat for the other original equation
7x-8y = -9
7*1-8*2 = -9
7-16 = -9
-9 = -9
Both equations are confirmed.


Another way to check the answer is to use a graphing tool like Desmos or GeoGebra to plot each of the original lines separately
The two lines 8x-7y = -6 and 7x-8y = -9 intersect at (1,2)
{{{drawing(500,500,-4,4,-4,4,
graph(500,500,-4,4,-4,4,-100,(-6-8x)/(-7),(-9-7x)/(-8)),
circle(1,2,0.05),
circle(1,2,0.08),
circle(1,2,0.10),
locate(1,1.92,"(1,2)")
)}}}
8x-7y = -6 in green
7x-8y = -9 in blue


Here is the link to the interactive Desmos graph
<a href = "https://www.desmos.com/calculator/uwnrw4zpj9">https://www.desmos.com/calculator/uwnrw4zpj9</a>
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