Solve for x and y: 2x - 7y = 31 3x + 5y = -31

Understand the Problem

The question requires solving a system of two linear equations with two variables, x and y. We need to find the values of x and y that satisfy both equations simultaneously.

Answer

$x = -2$ $y = -5$

Steps to Solve

Multiply the first equation by 5 and the second equation by 7 This will allow us to eliminate the y variable

$5 \cdot (2x - 7y) = 5 \cdot 31 \implies 10x - 35y = 155$ $7 \cdot (3x + 5y) = 7 \cdot (-31) \implies 21x + 35y = -217$

Add the two equations together Adding the two equations eliminates the $y$ term:

$(10x - 35y) + (21x + 35y) = 155 + (-217)$ $31x = -62$

Solve for x Divide both sides by 31:

$x = \frac{-62}{31} = -2$

Substitute x = -2 into the first original equation $2(-2) - 7y = 31$ $-4 - 7y = 31$
Solve for y Add 4 to both sides: $-7y = 35$ Divide by -7: $y = \frac{35}{-7} = -5$

$x = -2$ $y = -5$

More Information

The solution to the system of equations is $x = -2$ and $y = -5$. This means that the point (-2, -5) is the intersection of the two lines represented by the given equations.

Tips

A common mistake is making arithmetic errors when multiplying the equations or when substituting the value of x to solve for y. Another common mistake is forgetting to distribute the multiplication to all terms in the equation. It is important to double-check each step.

AI-generated content may contain errors. Please verify critical information

Thank you for voting!