how many solutions does this linear system have?\n$y = \\frac{2}{3}x + 2$\n$6x - 4y = -10$\none solution…

how many solutions does this linear system have?\n$y = \\frac{2}{3}x + 2$\n$6x - 4y = -10$\none solution: $(-0.6, -1.6)$\none solution: $(-0.6, 1.6)$\nno solution\ninfinite number of solutions

how many solutions does this linear system have?\n$y = \\frac{2}{3}x + 2$\n$6x - 4y = -10$\none solution: $(-0.6, -1.6)$\none solution: $(-0.6, 1.6)$\nno solution\ninfinite number of solutions

Answer

Explanation:

Step1: Substitute (y=\frac{2}{3}x + 2) into (6x-4y=-10)

Substitute (y) in the second equation: (6x-4(\frac{2}{3}x + 2)=-10)

Step2: Expand and simplify the equation

Expand: (6x-\frac{8}{3}x-8=-10) Combine like - terms: (\frac{18x - 8x}{3}=-10 + 8) (\frac{10x}{3}=-2)

Step3: Solve for (x)

Multiply both sides by (\frac{3}{10}): (x=-2\times\frac{3}{10}=-0.6)

Step4: Solve for (y)

Substitute (x = - 0.6) into (y=\frac{2}{3}x+2) (y=\frac{2}{3}\times(-0.6)+2) (y=-0.4 + 2=1.6)

Answer:

one solution: ((-0.6,1.6))