Answer:
2) only one equation needs to be multiplied by something if y is to be eliminated.
3) (x, y) = (-4, 0)
4) (5, 2) satisfies the first equation, but not the second.
Step-by-step explanation:
You want to answer some questions about the use of elimination to solve the system ...
The coefficients of x are not multiples of each other, so both equations must be multiplied by something to eliminate the x-variable.
The coefficient of y in the first equation is -9 times the coefficient of y in the second equation. This means only the second equation needs to be multiplied by something (9) to eliminate the y-variable. Michael's observation is correct.
(2x -9y) +9(5x +y) = (-8) +9(-20)
47x = -188 . . . . . . . . . . simplify; the y-variable has been eliminated
x = -4 . . . . . . . . . . . . divide by the coefficient of x
Y can be found by substitution:
2(-4) -9y = -8
-9y = 0 . . . . . . . . . add 8 to both sides
y = 0 . . . . . . . . divide by -9
The solution is (x, y) = (-4, 0).
The solution is shown in part (3), and does not match (5, 2). No further proof is needed.
We suspect you're being asked to substitute the given point into at least one of the equations to show the equation is not satisfied. Trying the values in the second equation, we have ...
5x +y = -20
5(5) +(2) = 27 ≠ -20 . . . . (5, 2) is not the solution
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Additional comment
The attached graph shows the offered point (5, 2) satisfies the first equation, so we choose to do the demonstration of part (4) using the second equation.
For standard form ax+by=c, the x- and y-intercepts are c/a and c/b, respectively. This means the intercepts for the first equation are a negative x-value and a positive y-value. The line will pass through the first quadrant.
For the second equation, both intercepts are negative, so the line has no presence in the first quadrant where the point (5, 2) is located.
