Question

I ONLY NEED 15 and 16!! PLEASE LABEL WHICH ONE YOU DO:)) TYSM!!

Answer 1

15. x-intercept = (-4, 0)

y-intercept = (0, 2.5)

16. A. An infinite number of solutions.

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:

`5x-8y=-20`

Substitute y = 0 into the given equation to find the x-intercept:

`\begin{aligned}y=0 \implies 5x-8(0) &=-20\\5x & = -20\\x & = (-20)/(5)\\x & = -4\end{aligned}`

Therefore, the x-intercept is (-4, 0).

Substitute x = 0 into the given equation to find the y-intercept:

`\begin{aligned}x=0 \implies 5(0)-8y &=-20\\-8y & = -20\\y & = (-20)/(-8)\\y & =2.5\end{aligned}`

Therefore, the y-intercept is (0, 2.5).

Question 16

Given system of equations:

`\begin{cases}3x-2y=14\\6x=4y+28\end{cases}`

Multiply the first equation by 2:

`\implies 2(3x-2y)=2(14)`

`\implies 6x-4y=28`

Add 4y to both sides:

`\implies 6x-4y+4y=4y+28`

`\implies 6x=4y+28`

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.