Question

Which shows the correct first step to solving the system of equations in the most efficient manner?

3x+2y-17
x+4y=19
O x=-4y+19
-2y+17
3
O x-
O4y=-x+19
Oy=-3x+17

Answer 1

(a) x = -4y +19

Explanation:

You want to know a good first step for solving the system of equations in an efficient manner.

• 3x +2y = 17
• x +4y = 19

Substitution

One way to solve these equations is by substitution. To do that, we typically write an expression for one of the variables in terms of the other. It is efficient to choose a variable that already has a coefficient of 1.

Here, a useful first step is to solve the second equation for x:

x = -4y +19

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Additional comment

Then the solution proceeds with substitution for x:

3(-4y +19) +2y = 17

-10y +57 = 17

-10y = -40

y = 4

x = -4(4) +19 = 3

The solution is (x, y) = (3, 4).

Another reasonable first step is to subtract the second equation from twice the first:

2(3x +2y) -(x +4y) = 2(17) -(19)

5x = 15

x = 3

3 +4y = 19 . . . . . . substitute for x in the second equation

y = (19 -3)/4 = 4

The "addition" or "elimination" method shown second is also shown using 5 steps, but these are generally more complicated steps than the ones shown for the "substitution" solution. It appears the substitution solution probably is "the most efficient" in this case.