Solve using the substitution method. Show your work. If a system has no solution or an infinite number of solutions, state this.

15x+9y=240; 6x+3y=90
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15x+9y=240 and 6x+3y=90. From the second equation 3y=90-6x, so 9y=3(90-6x)=270-18x. Substitute for 9y in the first equation: 15x+270-18x=240. Therefore 30=3x, so x=10. Substitute this value for x in the second equation: 60+3y=90, so 3y=30 and y=10. So x=y=10. So there is just one solution.

 

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