Question

My brain is starting to shut down at this point and I'm struggling to do this test. If I don't answer these questions my grade will fail and I will probably delete the app. Just hoping for someone to answer.

Explain how you solve the following system of linear equations by graphing, substitution, and elimination.

x+2y=63x-y=4

also if you solve this I'll give you brainless explain how to solve the following absolute value inequality and graph its solution. watch if it was an equation? what would you do differently?


`| (p)/(5) | + 6 \leqslant 8`
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Answer 1

Explanation:

To solve simultaneous equations graphically, you just sketch the lines on a graph and look for the point of intersection.

To sketch x + 2y = 63, just find the x and y intercepts. At the x-intercept, the y co-ordinate is always zero, so sub this in for y and solve for x:

⇒ x + 2(0) = 63

⇒ x = 63

So the x-intercept is (63, 0)

We can do the opposite for the y-intercept, as the x co-ordinate is always 0:

⇒ 0 + 2y = 63

⇒ 2y = 63

⇒ y = 31.5

So the y-intercept is (0, 31.5)

Just repeat for the second line, mark the intercepts on a graph, join them, and then look for the co-ordinates of where the lines intersect. These will be the values for x and y.

For substitution, we rearrange the subject for one equation, then sub its value into the other one.

So we can rearrange x - y = 4 to get x = y + 4. Now we sub the value of x here into the other equation:

⇒ (y + 4) + 2y = 63

Then just solve for y and plug it into either equation and find x.

For elimination, we can either add or subtract the two equations to eliminate a term. Here, we can subtract the two equations, to get rid of x:

⇒ x + 2y = 63

- x - y = 4

x - x is 0, so it is eliminated, 2y - - y is 2y + y which is 3y, and 63 -4 is 59.

So we're left with 3y = 59, which is easy to solve and then we plug it back in to solve for x.