Question 127163
Eq. 1: {{{4x - 9y = 14.5}}}
Eq. 2: {{{7y - 2x = -8.5}}}


Start by putting the equations into standard form:  {{{Ax+By=C}}}


Eq. 1: {{{4x - 9y = 14.5}}}
Eq. 2: {{{-2x + 7y = -8.5}}}


Let's start by eliminating the y variable.  We need a constant to multiply the first equation and another constant to multiply the second equation so that the coefficients on the y variables become additive inverses.  7 * -9 = -63 and 9 * 7 = 63.  That should work.


Eq. 3: {{{28x - 63y = 101.5}}}
Eq. 4: {{{-18x +63y = -76.5}}}


Now add the x terms together, the y terms together, and the constants together to create another equation that has a zero coefficient on y.


Eq. 5:  {{{10x + 0y = 25}}}
{{{10x=25}}}
{{{x=2.5}}}


Go back to the original set of equations:
Eq. 1: {{{4x - 9y = 14.5}}}
Eq. 2: {{{-2x + 7y = -8.5}}}


But this time, just multiply equation 2 by 2:
Eq. 6: {{{4x - 9y = 14.5}}}
Eq. 7: {{{-4x + 14y = -17}}}


Add the equations to eliminate x
Eq. 8: {{{0x+5y=-2.5}}}
{{{y=-.5}}}


Your solution set is (2.5,-.5)