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Oliver
07-11-2013, 05:52 PM
SAT mathematics Systems

How can we solve the following system of equations:

\begin{cases} 4x+ 2y=7 \\ x + y=3 \end{cases}

Thanks!!:D

kadence
07-11-2013, 05:59 PM
SAT math question about simultaneous equations

\begin{cases} 4x+ 2y=7 \\ x + y=3 \end{cases}

The method of substitution (step-by-step) is:

1.Solve one of the equations for one unknown in terms of the other.
2.Then, substitute that in the other equation.
3.That will yield one equation in one unknown, which we can solve.

So, in your case

\begin{cases} 4x+ 2y=7 \\ y=3-x \end{cases}

\begin{cases} 4x+ 2(3-x)=7 \\ y=3-x \end{cases}

\begin{cases} 4x+ 6-2x=7 \\ y=3-x \end{cases}

\begin{cases} 2x=7-6 \\ y=3-x \end{cases}

\begin{cases} 2x=1 \\ y=3-x \end{cases}

\begin{cases} x=\frac{1}{2} \\ y=3-\frac{1}{2}=\frac{6-1}{2}=\frac{5}{2} \end{cases}


Hope these help!!:D:D

Oliver
07-11-2013, 06:00 PM
Thank you Kadence!!