Question

honors algebra
solve a system what method?
name: dayami muñoz
period: 5

1. assuming you want to minimize the amount of work required, tell whether you would use the substitution or elimination method to solve each system. explain your answers. do not solve!

a. ( 3x + 2y = 18 )
( y = 3x )
b. ( 3x + y = -7 )
( x - y = 5 )
c. ( 3x - 2y = 0 )
( 9x + 8y = 7 )

1. which one of the following systems would be easier to solve using the substitution method? why?

a. ( 5x - 3y = 7 )
( 2x + 8y = 3 )
b. ( 7x + 2y = 4 )
( y = -3x + 1 )

Explanation:

For Question 1:

Part a:

One variable is already isolated ($y=3x$), so substitution requires no extra rearrangement steps, minimizing work.

Part b:

Either method works, but elimination is quick: multiply the second equation by 1 and add to eliminate $y$, or substitution is simple since $x$ can be isolated as $x=y+5$ easily. Elimination has minimal arithmetic here.

Part c:

Elimination is better: multiply the first equation by 3 to get $9x-6y=0$, then subtract from the second equation to eliminate $x$, avoiding fractions that would come from isolating a variable for substitution.

For Question 2:

Part b's system is easier for substitution:

In system b, $y$ is already isolated as $y=-3x+1$, so we can directly substitute this into the first equation without rearranging any terms. System a requires isolating a variable first, which adds extra steps.

Answer:

1.
a. Substitution; $y$ is already isolated.
b. Elimination; easy to eliminate a variable.
c. Elimination; avoids fractional coefficients.

2.
System b ($7x + 2y = 4$; $y = -3x + 1$); $y$ is already isolated, so substitution requires no extra rearrangement work.