Solve the system by the addition method, if possible. If a solution exists, give the value of x. $\left\{ \begin{array} { l }
4 ( x + y ) = y + 17 \
7 ( x + 1 ) = y + 18
\end{array} \right.$
A)2
B)5
C) 4
D) $- 1$
E) no solution

Question

Solve the system by the addition method, if possible. If a solution exists, give the value of x. $\left\{ \begin{array} { l } 
4 ( x + y ) = y + 17 \
7 ( x + 1 ) = y + 18
\end{array} \right.$
A)2
B)5
C) 4
D) $- 1$
E) no solution

Quizplus · Accepted Answer

2To solve the system by the addition method, we first simplify each equation:1. $4(x + y) = y + 17$Expanding, we get: $4x + 4y = y + 17$Subtracting $y$ from both sides: $4x + 3y = 17$2. $7(x + 1) = y + 18$Expanding, we get: $7x + 7 = y + 18$Subtracting $y$ from both sides and subtracting 18 from both sides: $7x - y = 11$Now, we have the system:$$\begin{align*}4x + 3y &= 17 \7x - y &= 11\end{align*}$$To use the addition method, we want to eliminate one of the variables. We can multiply the second equation by 3 to get the coefficients of $y$ to match:$$\begin{align*}4x + 3y &= 17 \21x - 3y &= 33\end{align*}$$Adding the two equations together to eliminate $y$:$$\begin{align*}4x + 21x &= 17 + 33 \25x &= 50 \x &= 2$$So, the value of $x$ is 2, which corresponds to choice A.

Solve the System by the Addition Method, If Possible {4(x+y)=y+177(x+1)=y+18\left\{ \begin{array} { l } 4 ( x + y ) = y + 17 \\7 ( x + 1 ) = y + 18\end{array} \right.{4(x+y)=y+177(x+1)=y+18​

Solve the System by the Addition Method, If Possible $\left\{ \begin{array} { l } 4 ( x + y ) = y + 17 \\7 ( x + 1 ) = y + 18\end{array} \right.$