which is the best approximation for the solution of the system of equations?\ny = -\\frac{2}{5}x + 1\ny = 3x…
which is the best approximation for the solution of the system of equations?\ny = -\\frac{2}{5}x + 1\ny = 3x - 2
Answer
Explanation:
Step1: Set the two equations equal
Since $y = y$, we set $-\frac{2}{5}x + 1=3x - 2$.
Step2: Get rid of the fraction
Multiply through by 5 to get $-2x + 5 = 15x-10$.
Step3: Isolate the $x$ - terms
Add $2x$ to both sides: $5=15x + 2x-10$, which simplifies to $5 = 17x-10$.
Step4: Solve for $x$
Add 10 to both sides: $15 = 17x$. Then $x=\frac{15}{17}\approx0.88$.
Step5: Find $y$ - value
Substitute $x\approx0.88$ into $y = 3x-2$. So $y=3\times0.88 - 2=2.64 - 2 = 0.64$.
Answer:
The best approximation for the solution is $(0.9,0.6)$ (rounded to one - decimal place).