$7 y+109=9 x+12 y$
Work out the value of $x$ when $y=11$
Answer (1)
Substitute y = 11 into the equation 7 y + 109 = 9 x + 12 y .
Simplify the equation to 77 + 109 = 9 x + 132 .
Combine constants and isolate x to get 54 = 9 x .
Solve for x by dividing both sides by 9, resulting in x = 6 .
Explanation
Understanding the Problem We are given the equation 7 y + 109 = 9 x + 12 y and we need to find the value of x when y = 11 .
Substitution First, substitute y = 11 into the equation: 7 ( 11 ) + 109 = 9 x + 12 ( 11 ) .
Simplification Now, simplify the equation: 77 + 109 = 9 x + 132 .
Combining Constants Combine the constants on the left side: 186 = 9 x + 132 .
Isolating the x term Subtract 132 from both sides of the equation: 186 − 132 = 9 x which simplifies to 54 = 9 x .
Solving for x Finally, divide both sides by 9 to solve for x : x = 9 54 = 6 .
Examples
This problem demonstrates how to solve a linear equation with two variables when one of the variables is given a specific value. In real life, this could be used to determine the cost of items when you know a relationship between the number of items and the total cost. For example, if the total cost of producing items is related to the number of items produced by a linear equation, and you know the cost when a certain number of items are produced, you can use this method to find the cost for any number of items.
