Answer:
[tex]x=2\\y=-1[/tex]
Step-by-step explanation:
Let:
[tex]3x+2y=4\hspace{5}(1)\\and\\4x+7y=1\hspace{5}(2)[/tex]
We need to eliminate one of the variables, so let's use elimination method. First multiply (1) by 4 and (2) by 3:
[tex]4*(1)\equiv\hspace{5}12x+8y=16\\3*(2)\equiv\hspace{5}12y+21y=3[/tex]
Now subtract 3*(2) from 4*(1) in order to eliminate x:
[tex]4*(1)-3*(2)\\12x-12x+8y-21y=16-3\\-13y=13[/tex]
Solving for y:
Multiplying both sides by -1/13
[tex]y=-\frac{13}{13} =-1[/tex]
Finally, replacing the value of y in (1)
[tex]3x+2*(-1)=4[/tex]
Solving for x:
add 2 to both sides:
[tex]3x=6[/tex]
Multiply both sides by 1/3:
[tex]x=\frac{6}{3} =2[/tex]
