If you determine that the x value of a system of linear equations is 1, what should you do next?
A. You can stop because you know there is no solution.
B. Substitute 1 for y in one of the equations, and solve for x.
C. Substitute 1 for x in one of the equations, and solve for y.
D. You can stop because you know that there is an infinite number of solutions.
Answer (2)
Substitute the known x-value, which is 1, into one of the equations.
Solve the equation for y to find the corresponding y-value.
The solution is the y-value that corresponds to x=1.
The next step is to substitute 1 for x in one of the equations, and solve for y. S u b s t i t u t e 1 f or x in o n eo f t h ee q u a t i o n s , an d so l v e f ory .
Explanation
Understanding the Problem We are given that the x-value of a system of linear equations is 1. Our goal is to find the corresponding y-value.
Finding the y-value To find the y-value, we substitute the known x-value into one of the equations in the system. This will give us an equation with only y as the unknown, which we can then solve.
Conclusion Therefore, the next step is to substitute 1 for x in one of the equations and solve for y.
Examples
Imagine you're baking a cake and the recipe tells you that for every cup of flour, you need half a cup of sugar. If you decide to use 2 cups of flour (your 'x' value), you substitute that value into the relationship to find out you need 1 cup of sugar (your 'y' value). Similarly, in linear equations, knowing one variable allows you to find the other by substituting it into the equation.
The next step is to substitute the known x-value of 1 into one of the equations to solve for y. This will yield the corresponding y-value that pairs with x. Therefore, choose option C: Substitute 1 for x in one of the equations, and solve for y.
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