2x + 4y = 12
3x - 5y = 10
a. write the equations in slope-intercept form. (show your work.)
b. graph the pair of linear equations.
c. use the graph to estimate the solution to the system of equations.
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1)     This format that the two equations are in is called Standard Form, and it's formula is Ax+By=C. Slope-Intercept Form is another form in which linear equations can be written. It's expressed as y=mx+b. See how in SIF (Slope intercept form), the "y" is isolated? All you have to do is isolate the "y" in both equations given to you.

2x+4y=12
-2x       -2x
4y=-2x+12
/4           /4
y=-1/2x+3

3x-5y=10
-3x       -3x
-5y=-3x+10
/-5         /-5
y=3/5x-2

2)     To graph SIF, you need to know what each aspect of the equation is. The formula is y=mx+b.

m stands for slope. A great way to remember it is rise/run (rise over run). Basically, the numerator in "m" is how far up you go to graph each point, and the denominator is how far left or right you go (remember, left is negative, right is positive). Let me give you an example. y=3/5x. In this formula, to graph each point, on the line, you'd go up 3, and to the right 5, then plot a point, then up 3, right 5, plot another one... you get it. What if the equation was y=3x though? The slope would be 3/1, or up 3, right one.

You know how to plot the points, but what coordinate do you start at? That's where the Y-Intercept comes into play. The Y-Intercept is basically where the line crosses the Y-axis. The b in the SIF formula is the y-intercept, and where you plot your very first coordinate on the line. If the SIF equation was y=1x+3, your first coordinate would be on the y axis, at an elevation of 3. Since the y-axis is at x=0, the coordinate would be (0,3). 

3)     Look at the graph now. Where do the lines cross? The x should be somewhere between 4 and 5, and the y is somewhere between 1.5 and 2. Therefor, your "estimation" should be something like (4.5,1.75)

I really hoped this helped you! It took a while to write so I'd appreciate if you'd choose the Brainliest answer -- thanks!

It's like discovering the answer to a puzzle. the purpose in solving an equation is to find the value or values of the variable that makes it a true statement. any value of the variable that makes the equation true is called a solution to the equation.