1. Solve by elimination method
4x - y = -3
y - 3 = 4x
Rewrite the equation in standard form:
4x - y = -3
4x - y = -3
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4x - y = -3
-4x + y = +3
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0 + 0 = 0
The equations are the same so there are many solution.
The graph are same line
Let us look at the graph to check if there is a solution
2. Solve by graphing method
x - y = 3
x + y = 1
To graph it easily, we will rewrite the equation in slope - intercept form
y = mx + b, where m = slope and b = y -intercept
x - y = 3 -------> y = x - 3 eq1, where m = 1 and b = -3
x + y = 1 -------> y = -x + 1 eq2, where m = -1 and b = 1
To graph eq1 the first point is (0,-3). use the slope the locate second point
m=1 means move 1 unit up and 1 unit right. then draw a line
To graph eq2 the first point is (0,1). use the slope to locate the 2nd point
m=-1 means move 1 unit down and 1 unit right or 1 unit up and 1 unit left
then draw a line.
the graph looks like this:
Solution is (2, -1). the graph intersect when x = 2 and y = -1.
3. Solve by addition method
We use this method so that one variable will be eliminated.
1/5x + 2/3y = -8/5 eq1
3x - y = 9 eq2
Simplify eq1. Mutiply LCD -15 each term (eq1 only)
3x + 10y = -24 eq1
3x - y = 9 eq2
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Notice, if we add the two equations, no variable will be eliminated
So we must multiply a certain number to do that
say we eliminate x,Multiply -1 eq2
3x + 10y = -24
-1(3x - y = 9)
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3x + 10y = -24
-3x + y = -9
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0 + 11y = -33 divide both sides by 11
y = -3
Substitute y = -3 to any of the equations
3x - y = 9
3x -(-3) = 9
3x + 3 = 9 subtract 3 both sides
3x = 6 Divide 3 both sides
x = 2
Solution is (2,-3). The graph intersect when x = 2 and y = -3
Checking:
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