Final answer:
To solve the system of equations by substitution, isolate one variable in terms of the other, substitute the value into the other equation, and solve the resulting equation.
Step-by-step explanation:
To solve the system of equations by substitution, we first solve one equation for one variable in terms of the other. From the first equation, we can isolate y by subtracting 2x from both sides, which gives us y = 7 - 2x. Now we substitute this value for y in the second equation:
6x(7 - 2x) = 15
Expanding and simplifying the equation, we get:
42x - 12x^2 = 15
Rearranging the equation and setting it equal to zero, we have:
12x^2 - 42x + 15 = 0
This quadratic equation can be factored or solved using the quadratic formula. Once we find the values of x, we can substitute them back into the original equation to find the corresponding values of y.
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