Question

Fill in the missing operation or missing equation to complete the table

Solve by elimination
connect top and bottom {5x-2y=17 Equation 1
{3x+7y=43Equation 2

Answer 1

2626262

Explanation:

x=722

Answer 2

Multiply Equation (1) by -3

Explanation:

The two equations are:

`$ 5x - 2y = 17 \hspace{20mm} \hdots  (1) $`

`$ 3x + 7y = 43 \hspace{20mm} \hdots (2) $`

In the first step, Equation (1) is multiplied by -3.

i.e., -3(5x - 2y = 17) = - 15x + 6y = - 51

The next instruction is to multiply Equation (2) by 5.

i.e., 5(3x + 7y = 43) = 15x + 35y = 215

We add the two new equations in the next step, to eliminate the variable x.

The sum is 41y = 164

Dividing by 41 through out, we get:

y = 4

Now, we solve for x.

To do this substitute the value of y in Equation (1) or (2).

We will substitute in (1).

Therefore, we get: 5x - 2(4) = 17

⇒ 5x = 25

⇒ x = 5

Therefore, (x, y) = (5, 4) is the solution to the equations given.