Question 263034
Well, your fist step simplified the two equations by clearing the fractions and that was a good move!
You ended up with:
1) {{{5x+2y = 8}}} and...
2) {{{4x-3y = 11}}} but simply adding these doesn't do you much good unless you eliminate one of the two variables in the process.
So the idea is to multiply one or both equations by a number that will result in having identical (or opposite in this case) coefficients for either variable so that when you add the two, per instructions, you will eliminate one of the variables.
So, looking at the two equations you got when you multiplied through by 6, you can make the coefficient of y equal to 6 and -6 respectively by multiplying equation 1) by 3 and equation 2) by 2.
{{{3(5x+2y) = 3(8)}}}
1a) {{{15x+6y = 24}}} and...
{{{2(4x-3y) = 2(11)}}}
2a) {{{8x-6y = 22}}}  Now when you add equations 1a) and 2a), you will eliminate the y variable.
{{{15x+6y = 24}}}
{{{8x-6y = 22}}} Add these.
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{{{23x = 46}}} Divide both sides by 23.
{{{highlight(x = 2)}}} Now substitute this into either one of the two equations 1) or 2) to solve for y.
I'll leave this for you to finish up!