Answer:
15. x-intercept = (-4, 0)
y-intercept = (0, 2.5)
16. A. An infinite number of solutions.
Step-by-step explanation:
Question 15
The x-intercepts are where the line crosses the x-axis, i.e. when y = 0.
The y-intercepts are where the line crosses the y-axis, i.e. when x = 0.
Given equation:
[tex]5x-8y=-20[/tex]
Substitute y = 0 into the given equation to find the x-intercept:
[tex]\begin{aligned}y=0 \implies 5x-8(0) &=-20\\5x & = -20\\x & = \dfrac{-20}{5}\\x & = -4\end{aligned}[/tex]
Therefore, the x-intercept is (-4, 0).
Substitute x = 0 into the given equation to find the y-intercept:
[tex]\begin{aligned}x=0 \implies 5(0)-8y &=-20\\-8y & = -20\\y & = \dfrac{-20}{-8}\\y & =2.5\end{aligned}[/tex]
Therefore, the y-intercept is (0, 2.5).
Question 16
Given system of equations:
[tex]\begin{cases}3x-2y=14\\6x=4y+28\end{cases}[/tex]
Multiply the first equation by 2:
[tex]\implies 2(3x-2y)=2(14)[/tex]
[tex]\implies 6x-4y=28[/tex]
Add 4y to both sides:
[tex]\implies 6x-4y+4y=4y+28[/tex]
[tex]\implies 6x=4y+28[/tex]
Therefore, the two equations are the same.
A system of linear equations has an infinite number of solutions when the graphs are the exact same line.
