Question 476503
For this problem I think elimination is the best way to find solution.
Step 1: Determine which variable you want to eliminate
Step 2: Find the least common multiple of the 2 coefficients.
Step 3: Multiply each equation by appropriate scale factor such that the coefficients will be equal but have opposite signs.
Step 4: Add the equations
Step 5: Solve the resulting single-variable equation.
Step 6: Substitute value back into one of the original equations to solve for 2nd variable. 
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{{{2x+3y=8}}}
{{{3x+2y=7}}}
Step 1: Eliminate x
Step 2: Least common multiple of 2 and 3 is 6.
Best way to do this is multiply them together...2*3=6
Step 3: Goal is to have 6x on top and -6x on bottom
Multiply top equation by 3... 2x*3 = 6x
Multiply bottom equation by -2... 3x*-2 = -6x
Equations change to: 
{{{6x + 9y = 24}}}
{{{-6x -4y = -14}}}
Step 4: Add equations, just add the coefficients in each column
Result:
{{{0x +5y = 10}}}
Step 5: solve for y
{{{5y = 10}}}
{{{y = 2}}}
Step 6: Pick 1 of the original equations and replace y with 2
{{{2x + 3(2) = 8}}}
{{{2x + 6 = 8}}}
{{{2x = 2}}}
{{{x = 1}}}
Then there is one unique solution of x =1 , y = 2.