Answer:
They both have an infinite number of solutions.
Step-by-step explanation:
Given system of equations:
a) 2x + 4y = 15
b) 6x + 12y = 45
Slope-intercept form: y = mx + b
<u>where:</u>
- m is the slope
- b is the y-intercept (when x = 0)
Rewrite <em>both</em> equations into slope-intercept form:
<em>a) 2x + 4y = 15 </em>
⇒ 2x + 4y = 15 [subtract 2x from both sides]
⇒ 2x - 2x + 4y = 15 - 2x
⇒ 4y = - 2x + 15 [divide both sides by 4]
⇒ 4y ÷ 4 = (-2x ÷ 4) + (15 ÷ 4)
<em>b) 6x + 12y = 45</em>
⇒ 6x + 12y = 45 [subtract 6x from both sides]
⇒ 6x - 6x + 12y = 45 - 6x
⇒ 12y = - 6x + 45 [divide both sides by 12]
⇒ 12y ÷ 12 = (-6x ÷ 12) + (45 ÷ 12)
New equations:
Both equations have the same slope (-½), and y-intercept (3.75). Therefore, they both have an infinite number of solutions.
System of equations can have the following:
<u><em>No Solution:</em></u> the same slope (both lines will be parallel)
<u><em>One Solution:</em></u> different slopes and different y-intercepts
<u><em>Infinitely Many Solutions:</em></u> the same slope and y-intercept
Learn more about system of equations here: