Question

solve the following of equations. express your answer as an order pair in the format (a,b) with no spaces between the numbers and symbols 2x + 7y = -1 4x - 3y = -19

Answer 1

Step 1:

In this question, we are given the following:

Solve the following equations.

Express your answer as an ordered pair in the format (a,b) with no spaces between the numbers and symbols:

`\begin{gathered} \text{2x + 7y = -1 -- equ 1} \\ 4\text{ x - 3y = -19 -equ 2} \end{gathered}`

Step 2:

We multiply equation 1 by 2, so we have that:

`\begin{gathered} 4\text{ x + 14y = -2 -- equation 3} \\ 4\text{ x - 3y = -19 -- equation 4} \end{gathered}`

Then, we evaluate equation 3 minus equation 4, we have that:

`\begin{gathered} 4x\text{ - 4x + 14y -(-3y) = -2 -(-19)} \\ 14y\text{ + 3y = -2 + 19} \\ 17y\text{ = 17} \\ \text{Divide both sides by 17, we have that:} \\ y\text{ =}(17)/(17) \\ y\text{ = 1} \end{gathered}`

Next, we put the value of y = 1 in equation 1, we have that:

`\begin{gathered} 2x+7y\text{ = -1} \\ 2x\text{ + 7 (1) = -1} \\ 2x\text{ + 7 = -1} \\ 2x\text{ = -1 - 7} \\ 2x\text{ = -8} \\ \text{Divide both sides by 2, we have that:} \\ x\text{ =}(-8)/(2) \\ x\text{ = -4} \end{gathered}`

CONCLUSION:

In ordered pair, the value of:

`(x,\text{ y ) = ( - 4, 1)}`