Answer:
Step-by-step 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.
