Question

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

-3x + 4y = -19.5

-3x + y = -10.5

Answer 1

second equation becomes
\[y=3x-10.5\]
substituting this into first equation
\[-3x + 4(3x-10.5) = -19.5\]\[-3x+12x-42=-19.5\]
solving for x
\[9x=22.5\]\[x=\frac{22.5}{9}=2.5\]
substitute this into second equation
\[-3(2.5) + y = -10.5\]\[y=-10.5+7.5\]\[y=-3\]
Hence the solution to the system is the point \[(2.5,-3)\]

Answer 2

The problem asked for the "elimination" method. Using the elimination method:
Subtract: -3x+4y=-19.5
_ -3x + y=-10.5
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3y=-9 solving for y getting y=-3 You eliminated the x and solved for y.
Now simply substitute the value of y (-3) into the second equation getting
-3x -3 = -10.5
-3x=-10.5+3
-3x=-7.5
x=2.5