Question 147780
Start with the given system of equations:



{{{system(y=5-3x,4x-5y=13)}}}



{{{y=5-3x}}} Start with the first equation.



{{{y=-3x+5}}} Rearrange the terms.



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{{{4x-5(-3x+5)=13}}} Now plug in {{{y=-3x+5}}} into the second equation.



{{{4x+15x-25=13}}} Distribute.



{{{19x-25=13}}} Combine like terms on the left side.



{{{19x=13+25}}} Add {{{25}}} to both sides.



{{{19x=38}}} Combine like terms on the right side.



{{{x=(38)/(19)}}} Divide both sides by {{{19}}} to isolate {{{x}}}.



{{{x=2}}} Reduce.



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Since we know that {{{x=2}}}, we can use this to find {{{y}}}.



{{{y=5-3x}}} Go back to the first equation.



{{{y=5-3(2)}}} Plug in {{{x=2}}}.



{{{y=-1}}} Simplify.


So the answer is {{{x=2}}} and {{{y=-1}}}.



This means that the system is consistent and independent.



Notice when we graph the equations, we see that they intersect at *[Tex \LARGE \left(2,-1\right)]. So this visually verifies our answer.



{{{drawing(500,500,-8,12,-8,12,
grid(1),
graph(500,500,-8,12,-8,12,5-3x,(13-4x)/(-5)),
circle(2,-1,0.05),
circle(2,-1,0.08),
circle(2,-1,0.10)
)}}} Graph of {{{y=5-3x}}} (red) and {{{4x-5y=13}}} (green)