Substituting with fractions
Master Substituting with fractions in Grade 10 math. ### Property To eliminate a denominator when solving, multiply every term on both sides of the equat.
Key Concepts
Property To eliminate a denominator when solving, multiply every term on both sides of the equation by the denominator.
Solve $\begin{cases} 3x + 2y = 3 \\ 4x 3y = 13 \end{cases}$. Isolate y: $y = \frac{ 3x 3}{2}$. Substitute into the second equation: $4x 3(\frac{ 3x 3}{2}) = 13$. Multiply all terms by 2 to get: $8x 3( 3x 3) = 26$. Solve $\begin{cases} 2x + 5y = 7 \\ 4y 3x = 1 \end{cases}$. Isolate x: $x = \frac{4y 1}{3}$. Substitute into the first equation: $2(\frac{4y 1}{3}) + 5y = 7$. Multiply all terms by 3 to get: $2(4y 1) + 15y = 21$.
Don't let fractions freak you out. When substitution leaves you with an equation containing a fraction, you have a secret weapon: the denominator. Multiply every single term on both sides of the equation by that denominator. This simple trick eliminates the fraction completely, leaving you with a much cleaner and friendlier equation that is far easier to solve.
Common Questions
What is Substituting with fractions?
### Property To eliminate a denominator when solving, multiply every term on both sides of the equation by the denominator. Think of a fraction in an equation like a tricky level in a video game. There’s a power-up to make it easier: multiplying by the denominator! This one move clears the...
How do you apply Substituting with fractions in practice?
Solve . Isolate y: . Substitute into the second equation: . Multiply all terms by 2 to get: . Solve . Isolate x: . Substitute into the first equation: . Multiply all terms by 3 to get: .
Why is Substituting with fractions important for Grade 10 students?
Think of this like two different road maps that end up describing the exact same route! When a system of equations has infinitely many solutions, it means both equations are just different ways of writing the same exact line. They are called coinciding lines. When you try to solve for or , all...