Answer :
To solve the system of equations using the comparison method, follow these steps:
You are given the system of equations:
1. [tex]\( x + y = 5 \)[/tex]
2. [tex]\( 2x + y = 7 \)[/tex]
The comparison method often involves isolating the same variable in two different equations and then setting those expressions equal to each other. However, in this context, we will use the substitution method, which ultimately leads to a comparison.
1. First, solve the first equation for [tex]\( y \)[/tex]:
[tex]\[ y = 5 - x \][/tex]
2. Substitute this expression for [tex]\( y \)[/tex] into the second equation:
- Second equation: [tex]\( 2x + y = 7 \)[/tex]
- Replace [tex]\( y \)[/tex] with [tex]\( 5 - x \)[/tex]:
[tex]\[ 2x + (5 - x) = 7 \][/tex]
3. Simplify the equation:
[tex]\[ 2x + 5 - x = 7 \][/tex]
[tex]\[ x + 5 = 7 \][/tex]
4. Solve for [tex]\( x \)[/tex]:
[tex]\[ x = 7 - 5 \][/tex]
[tex]\[ x = 2 \][/tex]
5. Use this value of [tex]\( x \)[/tex] to find [tex]\( y \)[/tex]:
[tex]\[ y = 5 - 2 \][/tex]
[tex]\[ y = 3 \][/tex]
Now, for the comparison method part, to identify which equation was reached by comparing isolated expressions, you would set the expressions [tex]\( y = 5 - x \)[/tex] and the rearranged form of the second equation:
- Rearrange [tex]\( 5 - x = 2x - 7 \)[/tex]
Thus, the equation that matches the result from the comparison method is:
[tex]\[ 5 - x = 2x - 7 \][/tex]
This corresponds to the choice [tex]\( 5-x=2x-7 \)[/tex].
You are given the system of equations:
1. [tex]\( x + y = 5 \)[/tex]
2. [tex]\( 2x + y = 7 \)[/tex]
The comparison method often involves isolating the same variable in two different equations and then setting those expressions equal to each other. However, in this context, we will use the substitution method, which ultimately leads to a comparison.
1. First, solve the first equation for [tex]\( y \)[/tex]:
[tex]\[ y = 5 - x \][/tex]
2. Substitute this expression for [tex]\( y \)[/tex] into the second equation:
- Second equation: [tex]\( 2x + y = 7 \)[/tex]
- Replace [tex]\( y \)[/tex] with [tex]\( 5 - x \)[/tex]:
[tex]\[ 2x + (5 - x) = 7 \][/tex]
3. Simplify the equation:
[tex]\[ 2x + 5 - x = 7 \][/tex]
[tex]\[ x + 5 = 7 \][/tex]
4. Solve for [tex]\( x \)[/tex]:
[tex]\[ x = 7 - 5 \][/tex]
[tex]\[ x = 2 \][/tex]
5. Use this value of [tex]\( x \)[/tex] to find [tex]\( y \)[/tex]:
[tex]\[ y = 5 - 2 \][/tex]
[tex]\[ y = 3 \][/tex]
Now, for the comparison method part, to identify which equation was reached by comparing isolated expressions, you would set the expressions [tex]\( y = 5 - x \)[/tex] and the rearranged form of the second equation:
- Rearrange [tex]\( 5 - x = 2x - 7 \)[/tex]
Thus, the equation that matches the result from the comparison method is:
[tex]\[ 5 - x = 2x - 7 \][/tex]
This corresponds to the choice [tex]\( 5-x=2x-7 \)[/tex].
