Substitution method

1) 3x + y = 7
4x + 2y = 16

2) 2x + 2y = 4
X - 2y = 0

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)

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

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



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

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



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