Mathematics

Mathematics

Problem

Solve the following system of equations using the *substitution* method: 3x+y=10x+2y=15\begin{aligned} 3x + y &= 10 \\ x + 2y &= 15 \end{aligned} Verify by substituting your values into both equations above.
Intuitive explanation

The substitution method works by isolating one variable in one equation, then plugging that expression into the other equation to eliminate it. Here, the first equation has yy with a coefficient of 1, making it the easiest to isolate—solve for yy in terms of xx, then substitute that expression into the second equation to find xx. Once you have xx, back-substitute to find yy, and check both values in the original equations.

Intuitive explanation

The substitution method works by isolating one variable in one equation, then plugging that expression into the other equation to eliminate it. Here, the first equation has yy with a coefficient of 1, making it the easiest to isolate—solve for yy in terms of xx, then substitute that expression into the second equation to find xx. Once you have xx, back-substitute to find yy, and check both values in the original equations.

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