Question

"Solve the system using elimination.

3x + 2y =17.
2x + 5y=26.

A (3, 4)
B. (2, 11/2)
C. (1/2, 5)
D. (1, 7)

Answer 1

The solution to the system of equations is found using the elimination method, and it yields the solution (3, 4), corresponding to option A.

Step-by-step explanation:

To solve the system of equations using elimination, we have the following two equations:

1. 3x + 2y = 17
2. 2x + 5y = 26

Let's multiply the first equation by 5 and the second equation by 2, which will allow us to eliminate y by subtracting the equations:

• (5)(3x + 2y) = (5)(17) → 15x + 10y = 85
• (2)(2x + 5y) = (2)(26) → 4x + 10y = 52

Now subtract the second modified equation from the first:

• (15x + 10y) - (4x + 10y) = 85 - 52
• 11x = 33
• x = 3

Substitute x = 3 into the original first equation:

• 3(3) + 2y = 17 → 9 + 2y = 17
• 2y = 8
• y = 4

Thus, the solution to the system is (3, 4), which corresponds to option A.

Answer 2

A.(3,4)

Step-by-step explanation:

To solve the system of equations using the elimination method, we want to manipulate the equations in a way that allows us to eliminate one of the variables when we add or subtract the equations.

Given system:

`\sf \begin{cases} 3x + 2y = 17 \quad (1) \\ 2x + 5y = 26 \quad (2) \end{cases}`

Multiply the first equation by 5 and the second equation by 2 to make the coefficients of
`\sf y` the same:

`\sf \begin{cases} 5(3x + 2y) = 5 * 17 \\ 2(2x + 5y) = 2 * 26 \end{cases}`

Simplify the equations:

`\sf \begin{cases} 15x + 10y = 85 \quad (3) \\ 4x + 10y = 52 \quad (4) \end{cases}`

Now, subtract equation (4) from equation (3) to eliminate
`\sf y`:

`\sf (15x + 10y) - (4x + 10y) = 85 - 52`

`\sf 11x = 33`

Now, solve for
`\sf x`:

`\sf x = (33)/(11) = 3`

Now that we have
`\sf x = 3`, substitute this into one of the original equations. Let's use the first equation (1):

`\sf 3(3) + 2y = 17`

`\sf 9 + 2y = 17`

Subtract 9 from both sides:

`\sf 9 + 2y-9 = 17-9`

`\sf 2y = 8`

Divide by 2:

`\sf (2y )/(2)=( 8)/(2)`

`\sf y = 4`

So, the solution to the system of equations is A.(3,4).