Question

Which ordered pair (a, b) is a solution to the given system of linear equations? -2a+3b=14

a-4b=3

Answer 1

The ordered pair (a, b) that is a solution to the given system of linear equations is approximately (-10.64, -2.43).

Step-by-step explanation:

To find the ordered pair (a, b) that is a solution to the given system of linear equations:

-2a + 3b = 14 --- (Equation 1)

4a - 4b = 3 --- (Equation 2)

We can solve this system of equations by either substitution or elimination method:

Substitution Method:

1. Solve Equation 1 for a:

• -2a = 14 - 3b
• a = (14 - 3b) / -2

Substitute the value of a in Equation 2:

• 4((14 - 3b) / -2) - 4b = 3
• (28 - 6b) / -2 - 4b = 3
• -28 + 6b - 8b = 6
• -14b = 34
• b = -34 / 14

Substitute the value of b back into Equation 1 to find a:

• -2a + 3(-34 / 14) = 14
• -2a - 102 / 14 = 14
• -28a - 102 = 196
• -28a = 298
• a = -298 / 28

Therefore, the ordered pair (a, b) that is a solution to the given system of linear equations is approximately (-10.64, -2.43).

Answer 2

The solution to the system of equations is
`\(a = -13\)` and
`\(b = -4\)`, so the ordered pair
`\((-13, -4)\)` is a solution to the given system of linear equations.

Let's solve the system of equations to find the values of a and b.

`\(-2a + 3b = 14\)`

`\(a - 4b = 3\)`

We can solve this system of equations using various methods, such as substitution or elimination. Let's use the substitution method:

From the second equation, we can express
`\(a\)` in terms of
`\(b\)`:

`\(a = 4b + 3\)`

Now substitute this expression for a into the first equation:

`\(-2a + 3b = 14\)`

`\(-2(4b + 3) + 3b = 14\)`

`\(-8b - 6 + 3b = 14\)`

`\(-5b - 6 = 14\)`

`\(-5b = 20\)`

`\(b = -4\)`

Now that we've found the value of b, let's substitute it back into
`\(a = 4b + 3\)` to find a:

`\(a = 4(-4) + 3\)`

`\(a = -16 + 3\)`

`\(a = -13\)`

Therefore, The answer is
`\(a = -13\)` and
`\(b = -4\)`.