Respuesta :
SOLUTION
We want to know which of the options forms a system of equation with
[tex]\begin{gathered} x+y=1 \\ give\text{ a solution of } \\ (-3,4) \end{gathered}[/tex]From the first option, we have
[tex]\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=\frac{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}[/tex]The second option we have
[tex]\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=\frac{5}{2} \\ We\text{ don't have }\frac{5}{2}\text{ as the first number in \lparen-3, 4\rparen} \\ So,\text{ this option is wrong too} \end{gathered}[/tex]The 3rd option, we have
[tex]\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=-\frac{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}[/tex]We got -3 and 4.
Hence the answer is the 3rd option
