Solve the system for $x$ and $y$.

$\begin{array}{l}
7 x+8 y=26 \\
-12 x-7 y=-58
\end{array}$

A. $(14,-9)$
B. $(-2.5)$
C. $(6,-2)$
D. $(-1,10)$

The solution to the system of equations is ( 6 , − 2 ) , meaning that x = 6 and y = − 2 . This was determined by using the elimination method to simultaneously solve the equations. Thus, the correct multiple-choice option is C.
;

Answered by Anonymous | 2025-07-04

Multiply the first equation by 12 and the second equation by 7 to prepare for elimination.
Add the modified equations to eliminate x and solve for y : 47 y = − 94 , so y = − 2 .
Substitute y = − 2 into the first original equation to solve for x : 7 x + 8 ( − 2 ) = 26 , so x = 6 .
The solution to the system of equations is ( 6 , − 2 ) ​ .

Explanation

Problem Analysis We are given a system of two linear equations with two variables, x and y . Our goal is to find the values of x and y that satisfy both equations simultaneously. The given equations are:

7 x + 8 y = 26 − 12 x − 7 y = − 58

Elimination Method We can solve this system using the method of elimination. Multiply the first equation by 12 and the second equation by 7 to eliminate x :

( 7 x + 8 y = 26 ) × 12 ⇒ 84 x + 96 y = 312 ( − 12 x − 7 y = − 58 ) × 7 ⇒ − 84 x − 49 y = − 406

Solving for y Now, add the two modified equations to eliminate x :

( 84 x + 96 y ) + ( − 84 x − 49 y ) = 312 + ( − 406 ) 47 y = − 94
Divide by 47 to solve for y :
y = 47 − 94 ​ = − 2

Solving for x Substitute the value of y = − 2 into the first original equation to solve for x :

7 x + 8 ( − 2 ) = 26 7 x − 16 = 26 7 x = 26 + 16 7 x = 42
Divide by 7 to solve for x :
x = 7 42 ​ = 6

Final Answer Therefore, the solution to the system of equations is x = 6 and y = − 2 . We can write this as the ordered pair ( 6 , − 2 ) .

Examples
Systems of equations are used in various real-world applications, such as determining the break-even point for a business, calculating the optimal mix of ingredients in a recipe, or modeling supply and demand in economics. For instance, suppose a bakery sells cakes and pies. Each cake requires 2 cups of flour and 1 cup of sugar, while each pie requires 1 cup of flour and 2 cups of sugar. If the bakery has 100 cups of flour and 80 cups of sugar available, we can set up a system of equations to determine how many cakes and pies the bakery can make. Solving this system helps the bakery optimize its production based on available resources.

Answered by GinnyAnswer | 2025-07-04