Solve the system of equations using substitution:
\[ y - 2x = -6 \]
\[ 5x - y = 9 \]
Answer (3)
\left \{ {\big{y-2x=-6} \atop\big {5x-y=9\ \ }} \right. \\\\ \left \{ {\big{y=2x-6\ \ \ \ \ \ \ \ \ \ } \atop\big {5x-(2x-6)=9\ \ }} \right. \\\\ \left \{ {\big{y=2x-6\ \ \ \ \ \ \ \ \ \ } \atop\big {5x-2x+6=9\ \ }} \right. \\\\ \left \{ {\big{y=2x-6\ \ } \atop\big {3x=3\ /:3 }} \right. \\\\ \left \{ {\big{y=2x-6 } \atop\big {x=1\ \ \ \ \ \ }} \right. \\\\ \left \{ {\big{y=-4 } \atop\big {x=1\ }} \right. \\\\
Ans.\ \left \{ {\big{x=1} \atop\big {y=-4}} \right. \ \ \ \Rightarrow\ \ \ point:\ \ (1;-4)
y-2x=-6 and 5x-y=9
step 1: isolate y in the first equation
y = 2x - 6
step 2: substitute the y value on the 2th equation:
5x-(2x-6)=9
step 3: solve the present equation:
5x - 2x + 6 = 9 3x = 9-6 3x = 3 x = 1
step 4: get the y value by replacing the value of x in y = 2x - 6: y = 2*1 - 6 y = 2 - 6 y = -4
S={1, -4}
To solve the system of equations, we isolate one variable and substitute it into the other equation. After simplification, we find that x = 1 and y = − 4 , resulting in the solution point (1, -4).
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