Question 240710
Given:
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Equation 1: {{{4X - 3Y = 17}}}
Equation 2: {{{5X + Y = 7}}}

Solution:
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Start by rewritting equation 2.  Since Y is by itself, solve for Y
Equation 2: {{{5X + Y = 7}}} Subtract 5X from both sides
{{{Y = 7 - 5X}}}

Now you can plug (7-5X) into equation 1 for Y
Equation 1: {{{4X - 3Y = 17}}}
{{{4X - 3*(7-5X) = 17}}} Simplify
{{{4X - 21 + 15X = 17}}} Simplify
{{{19X - 21 = 17}}} Add 21 to both sides
{{{19X = 38}}} Divide both sides by 19
{{{highlight(X = 2)}}}

To find Y, plug 2 in for X into the rewritten equation 2
{{{Y = 7 - 5X}}}
{{{Y = 7 - 5*(2)}}} Simplify
{{{Y = 7 - 10}}} Combine like terms
{{{highlight(Y = -3)}}}

Chesk Solution:
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Using X = 2 and Y = -3, solve equation 1
Equation 1: {{{4X - 3Y = 17}}}
{{{4*(2) - 3*(-3) = 17}}}
{{{8 + 9 = 17}}}
{{{17 = 17}}}