Solve the system of equations by using the addition method.
-$$\begin{array} { l }
5 x ^ { 2 } + 3 y ^ { 2 } = 95 \
x ^ { 2 } + 5 y ^ { 2 } = 129
\end{array}$$
A) $\{ ( 2,5 ) , ( 2 , - 5 ) , ( - 2,5 ) , ( - 2 , - 5 ) \}$
B) $\{ ( 2,5 ) , ( 2 , - 5 ) \}$
C) { }
D) $\{ ( 2,5 ) , ( - 2,5 ) \}$

Question

Solve the system of equations by using the addition method.
-$$\begin{array} { l } 
5 x ^ { 2 } + 3 y ^ { 2 } = 95 \
x ^ { 2 } + 5 y ^ { 2 } = 129
\end{array}$$
A) $\{ ( 2,5 ) , ( 2 , - 5 ) , ( - 2,5 ) , ( - 2 , - 5 ) \}$
B) $\{ ( 2,5 ) , ( 2 , - 5 ) \}$
C) {  }
D) $\{ ( 2,5 ) , ( - 2,5 ) \}$

Quizplus · Accepted Answer

To solve the system of equations by the addition method, we can multiply the equations by suitable coefficients to make the coefficients of one of the variables the same, then subtract or add the equations to eliminate that variable. However, in this case, it's more straightforward to directly solve the system as given:Given:$$5x^2 + 3y^2 = 95$$$$x^2 + 5y^2 = 129$$Subtract the second equation from the first:$$4x^2 - 2y^2 = -34$$$$2x^2 - y^2 = -17$$Now, we can express $y^2$ from one of the equations and substitute it into the other, or find another way to solve for $x$ and $y$. However, without going through all the algebraic steps here, the solution set will include pairs of $x$ and $y$ that satisfy both equations. Given the options, we can verify which pairs work.Checking the options, option A provides pairs that, when substituted into the original equations, satisfy both. For example, with $x = 2$ and $y = 5$:For the first equation:$$5(2)^2 + 3(5)^2 = 20 + 75 = 95$$For the second equation:$$(2)^2 + 5(5)^2 = 4 + 125 = 129$$This process can be repeated for the other pairs, confirming that they are solutions. Thus, the correct answer includes all four pairs, accounting for the positive and negative roots of $x$ and $y$.

Solve the System of Equations by Using the Addition Method 5x2+3y2=95x2+5y2=129\begin{array} { l } 5 x ^ { 2 } + 3 y ^ { 2 } = 95 \\x ^ { 2 } + 5 y ^ { 2 } = 129\end{array}5x2+3y2=95x2+5y2=129​

Solve the System of Equations by Using the Addition Method $\begin{array} { l } 5 x ^ { 2 } + 3 y ^ { 2 } = 95 \\x ^ { 2 } + 5 y ^ { 2 } = 129\end{array}$