-7x + y = -46 and -2x + 2y = -8

Solve the first equation for y : y = 7 x − 46 .
Substitute this expression into the second equation: − 2 x + 2 ( 7 x − 46 ) = − 8 .
Solve for x : x = 7 .
Substitute the value of x back into the equation to find y : y = 3 . The solution is x = 7 , y = 3 ​ .

Explanation

Analyze the problem We are given the following system of linear equations: − 7 x + y = − 46 − 2 x + 2 y = − 8 The goal is to find the values of x and y that satisfy both equations. We will use the substitution method to solve this system.

Solve for y in the first equation First, solve the first equation for y in terms of x :
y = 7 x − 46

Substitute into the second equation Substitute this expression for y into the second equation: − 2 x + 2 ( 7 x − 46 ) = − 8

Solve for x Simplify and solve the resulting equation for x :
− 2 x + 14 x − 92 = − 8 12 x = 84 x = 12 84 ​ x = 7

Solve for y Substitute the value of x back into the equation y = 7 x − 46 to find the value of y :
y = 7 ( 7 ) − 46 y = 49 − 46 y = 3

State the solution Therefore, the solution to the system of equations is x = 7 and y = 3 .


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 traffic flow in a city. For example, a company might use a system of equations to determine the number of units they need to sell to cover their costs and start making a profit. Understanding how to solve systems of equations is essential for making informed decisions in many fields.

Answered by GinnyAnswer | 2025-07-03

The solution to the system of equations − 7 x + y = − 46 and − 2 x + 2 y = − 8 is x = 7 and y = 3 . This is found using the substitution method to solve for one variable and substituting back to find the other. The point (7, 3) indicates where the two lines intersect on a graph.
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Answered by Anonymous | 2025-07-04