Linear Equation

Question

Solve the systems of linear equations by using the method of substitution. If the system is consistent, inconsistent, or dependent, say so in your answer. 3x-2y=5       x+3y=17

Answer 1

First, we know that we have 3x-2y=5 and x+3y=17. If we are told to use substitution, then the easiest substitution we can make is by putting or isolating x by itself for x+3y=17. Therefore, x=17-3y. Then, we can substitute that in for 3x-2y=5 and make it 3(17-3y)-2y=5. At this point, we can solve for y by distributing the parenthesis, 51-9y-2y=5, and then solving, -11y=-46; the y would be equal to 46/11. Now, we can solve for x by substituting 46/11 for y, 3x-2(46/11)=5. x would be equal to 49/11. If we check these two fractions with the second equation x+3y=17, 49/11+3(46/11)=17, the equation would be equal to 17. In terms of this substitution method, it is definitely dependent on the system of these two linear equations; I am unsure of what consistency they are asking about, but say for example x=1 and y=-1. 3(1)-2(-1)=5 is true, but not true for 1+3(-1)=17, so x and y values that holds true for the first equation may not hold true for the second equation, emphasizing on inconsistencies, or inconsistent in this case.