1.

{{:(4x-5y=10),(2x+3y=-6):} If the solution to the system of equations above is (x,y), what is the value of y?

Answer»

`-2`
`-1`
1
2

Solution :Both variables have DIFFERENT coefficients in the two equations, but you can convert the 2x in the SECOND equation to 4x by multiplying the entire second equation by 2:
`2 (2x+3y=-6)`
`4x + 6y=-12`
Now that the coefficients for one variable are the same, SUBTRACT the second equation from the first to eliminate the x variable. (Note that if the x-coeffcients were 4 and -4, you would add the equations instead of SUBTRACTING.)
`4x-5y=10`
`(-(4x+ 6y=-12))/(0x-11 y =22)`
Solve this equation for y:
`-11=22`
`y = -2`
(A) is the correct answer. If the question asked for x instead of y, you would now substitute -2 into either of the original equations and solve for x. (For the record, `x =0.)`


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