Solve the system of equations using substitution.

1. \(9x - 2y = -21\)
2. \(2x + 3y = 16\)

9x=-21+2y \\\\ => \boxed{x=\frac{2y-21}{9}} \\\\ 2x+3y=16 \\\\ 2*\frac{2y-21}{9}+3y^{(9}=16^{(9} \\\\ 2(2y-21)+27y=144 \\\\ 4y-42+27y=144 \\\\ 31y=144+42 \\\\ 31y=186 \\\\ \boxed{y=\frac{186}{31}=6} \\\\ x=\frac{2*6-21}{9} \\\\ x=\frac{12-21}{9} \\\\ x=\frac{-9}{9} \\\\ \boxed{x=-1}"> 9 x − 2 y = − 21 <=> 9 x = − 21 + 2 y => x = 9 2 y − 21 ​ ​ 2 x + 3 y = 16 2 ∗ 9 2 y − 21 ​ + 3 y ( 9 = 1 6 ( 9 2 ( 2 y − 21 ) + 27 y = 144 4 y − 42 + 27 y = 144 31 y = 144 + 42 31 y = 186 y = 31 186 ​ = 6 ​ x = 9 2 ∗ 6 − 21 ​ x = 9 12 − 21 ​ x = 9 − 9 ​ x = − 1 ​

Answered by mariamikayla | 2024-06-10

To solve the system of equations, start by rewriting one equation in terms of one variable. Substitute that expression into the other equation to find the values for both variables, resulting in x = − 1 and y = 6 . The solution is therefore the point ( − 1 , 6 ) .
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Answered by mariamikayla | 2024-12-26