Answer :
To solve this problem, we need to determine which ordered pairs satisfy each of the given equations. Let's go through each equation one by one and test the given ordered pairs to see if they satisfy the equations.
### 1. Equation: [tex]\( -4y = 3x + 1 \)[/tex]
We will substitute each ordered pair [tex]\( (x, y) \)[/tex] into the equation and check if it holds true.
1. [tex]\( (2, -4) \)[/tex]:
[tex]\[ -4(-4) = 3(2) + 1 \implies 16 \neq 7 \][/tex]
This pair does not satisfy the equation.
2. [tex]\( (2, 1) \)[/tex]:
[tex]\[ -4(1) = 3(2) + 1 \implies -4 \neq 7 \][/tex]
This pair does not satisfy the equation.
3. [tex]\( (-1, -1) \)[/tex]:
[tex]\[ -4(-1) = 3(-1) + 1 \implies 4 \neq -2 \][/tex]
This pair does not satisfy the equation.
4. [tex]\( (1, -1) \)[/tex]:
[tex]\[ -4(-1) = 3(1) + 1 \implies 4 = 4 \][/tex]
This pair satisfies the equation.
5. [tex]\( (1, 2) \)[/tex]:
[tex]\[ -4(2) = 3(1) + 1 \implies -8 \neq 4 \][/tex]
This pair does not satisfy the equation.
Thus, the solution for the first equation [tex]\( -4y = 3x + 1 \)[/tex] is [tex]\( (1, -1) \)[/tex].
### 2. Equation: [tex]\( y = -5x + 6 \)[/tex]
We will substitute each ordered pair [tex]\( (x, y) \)[/tex] into the equation and check if it holds true.
1. [tex]\( (2, -4) \)[/tex]:
[tex]\[ -4 = -5(2) + 6 \implies -4 = -10 + 6 \implies -4 = -4 \][/tex]
This pair satisfies the equation.
2. [tex]\( (2, 1) \)[/tex]:
[tex]\[ 1 = -5(2) + 6 \implies 1 \neq -10 + 6 \][/tex]
This pair does not satisfy the equation.
3. [tex]\( (-1, -1) \)[/tex]:
[tex]\[ -1 = -5(-1) + 6 \implies -1 \neq 5 + 6 \][/tex]
This pair does not satisfy the equation.
4. [tex]\( (1, -1) \)[/tex]:
[tex]\[ -1 = -5(1) + 6 \implies -1 \neq -5 + 6 \][/tex]
This pair does not satisfy the equation.
5. [tex]\( (1, 2) \)[/tex]:
[tex]\[ 2 = -5(1) + 6 \implies 2 \neq -5 + 6 \][/tex]
This pair does not satisfy the equation.
Thus, the solution for the second equation [tex]\( y = -5x + 6 \)[/tex] is [tex]\( (2, -4) \)[/tex].
### 3. Equation: [tex]\( 7y - 2x = 3 \)[/tex]
We will substitute each ordered pair [tex]\( (x, y) \)[/tex] into the equation and check if it holds true.
1. [tex]\( (2, -4) \)[/tex]:
[tex]\[ 7(-4) - 2(2) = 3 \implies -28 - 4 \neq 3 \][/tex]
This pair does not satisfy the equation.
2. [tex]\( (2, 1) \)[/tex]:
[tex]\[ 7(1) - 2(2) = 3 \implies 7 - 4 = 3 \][/tex]
This pair satisfies the equation.
3. [tex]\( (-1, -1) \)[/tex]:
[tex]\[ 7(-1) - 2(-1) = 3 \implies -7 + 2 \neq 3 \][/tex]
This pair does not satisfy the equation.
4. [tex]\( (1, -1) \)[/tex]:
[tex]\[ 7(-1) - 2(1) = 3 \implies -7 - 2 \neq 3 \][/tex]
This pair does not satisfy the equation.
5. [tex]\( (1, 2) \)[/tex]:
[tex]\[ 7(2) - 2(1) = 3 \implies 14 - 2 \neq 3 \][/tex]
This pair does not satisfy the equation.
Thus, the solution for the third equation [tex]\( 7y - 2x = 3 \)[/tex] is [tex]\( (2, 1) \)[/tex].
### Summary
1. [tex]\( -4y = 3x + 1 \)[/tex] is satisfied by [tex]\( (1, -1) \)[/tex].
2. [tex]\( y = -5x + 6 \)[/tex] is satisfied by [tex]\( (2, -4) \)[/tex].
3. [tex]\( 7y - 2x = 3 \)[/tex] is satisfied by [tex]\( (2, 1) \)[/tex].
There you have a detailed step-by-step solution with the matching ordered pairs.
### 1. Equation: [tex]\( -4y = 3x + 1 \)[/tex]
We will substitute each ordered pair [tex]\( (x, y) \)[/tex] into the equation and check if it holds true.
1. [tex]\( (2, -4) \)[/tex]:
[tex]\[ -4(-4) = 3(2) + 1 \implies 16 \neq 7 \][/tex]
This pair does not satisfy the equation.
2. [tex]\( (2, 1) \)[/tex]:
[tex]\[ -4(1) = 3(2) + 1 \implies -4 \neq 7 \][/tex]
This pair does not satisfy the equation.
3. [tex]\( (-1, -1) \)[/tex]:
[tex]\[ -4(-1) = 3(-1) + 1 \implies 4 \neq -2 \][/tex]
This pair does not satisfy the equation.
4. [tex]\( (1, -1) \)[/tex]:
[tex]\[ -4(-1) = 3(1) + 1 \implies 4 = 4 \][/tex]
This pair satisfies the equation.
5. [tex]\( (1, 2) \)[/tex]:
[tex]\[ -4(2) = 3(1) + 1 \implies -8 \neq 4 \][/tex]
This pair does not satisfy the equation.
Thus, the solution for the first equation [tex]\( -4y = 3x + 1 \)[/tex] is [tex]\( (1, -1) \)[/tex].
### 2. Equation: [tex]\( y = -5x + 6 \)[/tex]
We will substitute each ordered pair [tex]\( (x, y) \)[/tex] into the equation and check if it holds true.
1. [tex]\( (2, -4) \)[/tex]:
[tex]\[ -4 = -5(2) + 6 \implies -4 = -10 + 6 \implies -4 = -4 \][/tex]
This pair satisfies the equation.
2. [tex]\( (2, 1) \)[/tex]:
[tex]\[ 1 = -5(2) + 6 \implies 1 \neq -10 + 6 \][/tex]
This pair does not satisfy the equation.
3. [tex]\( (-1, -1) \)[/tex]:
[tex]\[ -1 = -5(-1) + 6 \implies -1 \neq 5 + 6 \][/tex]
This pair does not satisfy the equation.
4. [tex]\( (1, -1) \)[/tex]:
[tex]\[ -1 = -5(1) + 6 \implies -1 \neq -5 + 6 \][/tex]
This pair does not satisfy the equation.
5. [tex]\( (1, 2) \)[/tex]:
[tex]\[ 2 = -5(1) + 6 \implies 2 \neq -5 + 6 \][/tex]
This pair does not satisfy the equation.
Thus, the solution for the second equation [tex]\( y = -5x + 6 \)[/tex] is [tex]\( (2, -4) \)[/tex].
### 3. Equation: [tex]\( 7y - 2x = 3 \)[/tex]
We will substitute each ordered pair [tex]\( (x, y) \)[/tex] into the equation and check if it holds true.
1. [tex]\( (2, -4) \)[/tex]:
[tex]\[ 7(-4) - 2(2) = 3 \implies -28 - 4 \neq 3 \][/tex]
This pair does not satisfy the equation.
2. [tex]\( (2, 1) \)[/tex]:
[tex]\[ 7(1) - 2(2) = 3 \implies 7 - 4 = 3 \][/tex]
This pair satisfies the equation.
3. [tex]\( (-1, -1) \)[/tex]:
[tex]\[ 7(-1) - 2(-1) = 3 \implies -7 + 2 \neq 3 \][/tex]
This pair does not satisfy the equation.
4. [tex]\( (1, -1) \)[/tex]:
[tex]\[ 7(-1) - 2(1) = 3 \implies -7 - 2 \neq 3 \][/tex]
This pair does not satisfy the equation.
5. [tex]\( (1, 2) \)[/tex]:
[tex]\[ 7(2) - 2(1) = 3 \implies 14 - 2 \neq 3 \][/tex]
This pair does not satisfy the equation.
Thus, the solution for the third equation [tex]\( 7y - 2x = 3 \)[/tex] is [tex]\( (2, 1) \)[/tex].
### Summary
1. [tex]\( -4y = 3x + 1 \)[/tex] is satisfied by [tex]\( (1, -1) \)[/tex].
2. [tex]\( y = -5x + 6 \)[/tex] is satisfied by [tex]\( (2, -4) \)[/tex].
3. [tex]\( 7y - 2x = 3 \)[/tex] is satisfied by [tex]\( (2, 1) \)[/tex].
There you have a detailed step-by-step solution with the matching ordered pairs.
