Question

monday
substitution. what is the value of y if x = 4?
\\( y = 5x + 12 \\)
\\( y = \frac{3}{2}x - 10 \\)
which equation is true when y = 10 and x = 2?
a) \\( y = \frac{1}{2}x + 5 \\)
b) \\( y = 3x - 5 \\)
how many solutions? solve if one solution.
\\( 3x - 5 = 7 - x \\)

Explanation:

Step1: Substitute $x=4$ into $y=5x+12$

$y=5(4)+12=20+12=32$

Step2: Substitute $x=4$ into $y=\frac{3}{2}x-10$

$y=\frac{3}{2}(4)-10=6-10=-4$

Step3: Test $x=2,y=10$ in a)

$y=\frac{1}{2}(2)+5=1+5=6
eq10$

Step4: Test $x=2,y=10$ in b)

$y=3(2)-5=6-5=1
eq10$

Step5: Test $x=2,y=10$ in c)

$y=-5(2)+20=-10+20=10$

Step6: Solve $3x-5=7-x$, collect x terms

$3x+x=7+5$

Step7: Simplify and solve for x

$4x=12 \implies x=\frac{12}{4}=3$

Answer:

1. For $y=5x+12$ when $x=4$: $y=32$
2. For $y=\frac{3}{2}x-10$ when $x=4$: $y=-4$
3. True equation: c) $y=-5x+20$
4. For $3x-5=7-x$: 1 solution, $x=3$