Substitution Method

1)
\[
\begin{cases}
3x + y = 7 \\
4x + 2y = 16
\end{cases}
\]

2)
\[
\begin{cases}
2x + 2y = 4 \\
x - 2y = 0
\end{cases}
\]

1. ) { 3 x + y = 7/ ∗ ( − 2 ) 4 x + 2 y = 16 ​ { − 6 x − 2 y = − 14 4 x + 2 y = 16 ​ − − − − − − − − 2 x = 2/ : ( − 2 ) x = − 2
3 ∗ ( − 1 ) + y = 7 − 3 + y = 7 y = 7 + 3 y = 10 { x = − 1 y = 10 ​
2. ) { 2 x + 2 y = 4 x − 2 y = 0 ​ − − − − − − − − 3 x = 4/ : 3 x = 3 4 ​ 2 ∗ 3 4 ​ + 2 y = 4
2 y = 3 12 ​ − 3 8 ​ 2 y = 3 4 ​ / ∗ ( 2 1 ​ ) y = 3 2 ​ { x = 3 4 ​ y = 3 2 ​ ​

Answered by Anonymous | 2024-06-10

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

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)

Answered by HannahN | 2024-06-10

We solved two systems of equations using the substitution method. The solutions are (-1, 10) for the first system and (4/3, 2/3) for the second system. This method involves isolating one variable and substituting it into the other equation to find the values of both variables.
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Answered by Anonymous | 2024-09-30