Final answer:
The question pertains to Mathematics, specifically 10th-grade algebra involving simultaneous equations. This area of math calls for the use of substitution, elimination, or graphical methods to find variable values that satisfy multiple equations concurrently.
Step-by-step explanation:
The subject of this question is Mathematics at the Grade 10 level, specifically focusing on simultaneous equations which falls under the broader category of Algebra. While we cannot provide specific premium content from White Rose Maths, we can certainly discuss the topic of simultaneous equations and how to solve them. Simultaneous equations involve finding the values of variables that satisfy multiple equations at the same time. To solve these, one can use methods such as substitution, elimination, or graphical solutions.
For example, consider the two equations:
- y = 2x + 3
- y = -x + 5
One way to solve these simultaneous equations is by substitution. First, you can take the expression for y from the first equation and substitute it into the second, which would give you an equation with a single variable. Once you determine the value of x, you plug it back into one of the original equations to find the value of y.
An alternative method is elimination, where you manipulate the equations so that when they are added together, one of the variables eliminates itself, enabling you to solve for the remaining variable. After finding one variable, substitute it back into one of the original equations to find the other variable. Both substitution and elimination require an understanding of algebraic manipulation and the ability to work with equations.
Key steps for solving simultaneous equations:
- Identify the two equations provided.
- Choose a method: substitution or elimination.
- Carry out the necessary algebraic manipulations.
- Solve for one variable.
- Substitute the found value into one of the original equations to find the other variable.
- Check the solution by substituting both variables into both original equations.