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Tema [17]
3 years ago
8

What is the solution to the system of equations?

Mathematics
1 answer:
kap26 [50]3 years ago
7 0

Answer:

\large\boxed{\left(7,\ \dfrac{13}{3}\right)}

Step-by-step explanation:

You must use the algebraic method: substitution or elimination.

I will solve a given system of equations the substitution method.

\left\{\begin{array}{ccc}y=\dfrac{1}{3}x+2&(1)\\\\y=\dfrac{4}{3}x-5&(2)\end{array}\right\qquad\text{substitute (2) to (1)}\\\\\dfrac{4}{3}x-5=\dfrac{1}{3}x+2\qquad\text{multiply both sides by 3}\\\\3\!\!\!\!\diagup^1\cdot\dfrac{4}{3\!\!\!\!\diagup_1}x-(3)(5)=3\!\!\!\!\diagup^1\cdot\dfrac{1}{3\!\!\!\!\diagup_1}x+(3)(2)\\\\4x-15=x+6\qquad\text{add 15 to both sides}\\\\4x=x+21\qquad\text{subtract x from both sides}\\\\3x=21\qquad\text{divide both sides by 3}\\\\x=7\\\\\text{put the value of x to the first equation}\\\\y=\dfrac{1}{3}\cdot7+2\\\\y=\dfrac{7}{3}+\dfrac{6}{3}\\\\y=\dfrac{13}{3}

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Answer:

Step-by-step explanation:

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(Just a fun fact:  Those expressions come from the quadratic formula that help us to factor a quadratic equation.)

Filling in for h:

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