Question

Which equation together

Answer 1

We want to know which of the options forms a system of equation with

`\begin{gathered} x+y=1 \\ give\text{ a solution of } \\ (-3,4) \end{gathered}`

From the first option, we have

`\begin{gathered} x+y=1 \\ y=x \\ putting\text{ y = x into the equation above, we have } \\ x+y=1 \\ x+x=1 \\ 2x=1 \\ x=(1)/(2) \\ We\text{ don't have this as x, that is the first value in \lparen-3, 4\rparen} \\ Hence\text{ this option is wrong } \end{gathered}`

The second option we have

`\begin{gathered} x+y=1 \\ x-y=4 \\ combing\text{ both to eliminate y, we have } \\ (x+x)+(y-y)=1+4 \\ 2x+0=5 \\ 2x=5 \\ x=(5)/(2) \\ We\text{ don't have }(5)/(2)\text{ as the first number in \lparen-3, 4\rparen} \\ So,\text{ this option is wrong too} \end{gathered}`

The 3rd option, we have

`\begin{gathered} x+y=1 \\ y=x+7 \\ So\text{ replace x + 7 with y in the first equation, we have } \\ x+y=1 \\ x+x+7=1 \\ 2x=1-7 \\ 2x=-6 \\ x=-(6)/(2) \\ x=-3 \\ Putting\text{ -3 into the first equation, we have } \\ x+y=1 \\ -3+y=1 \\ y=1+3 \\ y=4 \end{gathered}`

We got -3 and 4.

Hence the answer is the 3rd option