Question

Substitution method

Answer 1

1. y=7-3x
4x+2(7-3x)=16
4x+14-6x=16
-2x=2
x=-1
-3+y=7
y=10
(-1,10)

2. x=2y
2(2y)+2y=4
4y+2y=4
6y=4
y=2/3
x-2(2/3)=0
x-4/3=0
x=4/3
(4/3,2/3)

Answer 2

$1.)\\ \\\begin{cases}3x + y = 7 /*(-2)\\ 4x + 2y = 16 \end{cases} \\ \\\begin{cases}-6x-2y =-14 \\ 4x + 2y = 16 \end{cases}\\-------\\-2x=2/:(-2)\\ \\x=-2$

$3*(-1) + y = 7\\ \\-3+y=7\\ \\y=7+3\\ \\y=10\\ \\\begin{cases}x=-1\\ y=10 \end{cases}$



$2.)\\ \\\begin{cases}2x + 2y = 4 \\x - 2y = 0 \end{cases} \\-------- \\ 3x=4/:3\\ \\x=\frac{4}{3}\\ \\2*\frac{4}{3}+ 2y = 4$

$2y=\frac{12}{3}-\frac{8}{3}\\ \\2y=\frac{4}{3}/*(\frac{1}{2})\\ \\y=\frac{2}{3}\\ \\\begin{cases}x=\frac{4}{3} \\y=\frac{2}{3}\end{cases}$