$\begin{array}{r}y \stackrel{*}{=}-2 x \\ 5 x-7 y=-38\end{array}$

Substitute y = − 2 x into the second equation.
Simplify the equation: 5 x − 7 ( − 2 x ) = − 38 ⇒ 19 x = − 38 .
Solve for x : x = − 2 .
Substitute x = − 2 into y = − 2 x to find y = 4 . The solution is x = − 2 , y = 4 ​ .

Explanation

Analyze the problem We are given a system of two linear equations:

Equation 1: y = − 2 x Equation 2: 5 x − 7 y = − 38
Our goal is to find the values of x and y that satisfy both equations. We can use the substitution method to solve this system.

Substitution Substitute the expression for y from Equation 1 into Equation 2:

5 x − 7 ( − 2 x ) = − 38

Simplify the equation Simplify the equation:

5 x + 14 x = − 38
19 x = − 38

Solve for x Solve for x :

x = 19 − 38 ​
x = − 2

Solve for y Now that we have the value of x , we can substitute it back into Equation 1 to find the value of y :

y = − 2 ( − 2 )
y = 4

State the solution Therefore, the solution to the system of equations is x = − 2 and y = 4 .

Examples
Systems of equations are used in many real-world applications, such as determining the break-even point for a business, calculating the optimal mix of ingredients in a recipe, or modeling traffic flow. For example, suppose a bakery sells cookies for $2 each and brownies for $3 each. If they want to make $100 in sales and sell twice as many cookies as brownies, they can set up a system of equations to determine how many of each item they need to sell. Solving this system helps them plan their production efficiently.

Answered by GinnyAnswer | 2025-07-03

To solve the system of equations, we substitute y = − 2 x into the second equation, simplifying to find x = − 2 . We then find y by substituting x back into the first equation, yielding y = 4 . The solution to the system is ( − 2 , 4 ) .
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Answered by Anonymous | 2025-07-04