SOLUTION: how do you solve for a system of linear equations y=2/3x-1 and y=-x+4

Question 73645This question is from textbook
: how do you solve for a system of linear equations y=2/3x-1 and y=-x+4 This question is from textbook

Found 2 solutions by checkley75, bucky:
Answer by checkley75(3666) (Show Source): You can put this solution on YOUR website!
SINCE Y=-X+4 THEN WE SUBSTITUTE (-X+4) FIR Y IN THE OTHER EQUATION WE GET
-X+4=2X/3-1
-X-2X/3=-1-4
(-3X-2X)/3=-5
-5X/3=-5 NOW CROSS MULTIPLY
-5X=-15
X=-15/-5
X=3 ANSWER. NOW SUBSTITUTE 3 FOR X & SOLVE FOR Y
Y=-3+4
Y=1 ANSWER.
PROOF
1=2/3*3-1
1=2-1
1=1
GRAPHS FOLLOW
(graph 300x300 pixels, x from -10 to 10, y from -10 to 10, of TWO functions y = 2x/3 -1 and y = -x +4).
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given:
.
and

.
You could graph the equations and see where the graphs cross. That crossing point contains
the values of x and y that are common solutions for both equations.
.
But a mathematical way to solve it could begin like this. Notice that the left sides of
both these equations are equal ... they are both y. Therefore, the right sides of these
equations must be equal also. So set them equal and this equation becomes:
.

.
To make things easier, get rid of the denominator on the left side by multiplying all the
terms in this equation (both sides) by 3. When you do that the equation becomes:
.

.
Get the terms with the variable x on the left side and collect the numbers on the right side.
To do this let's eliminate the -3x on the right side by adding +3x to it to cancel it.
But if we add +3x to the right side, we must also add +3x to the left side. Note that
when we add +3x to the left side, it will combine with the +2x that is already there to
make a total of 5x. So as a result of adding +3x to both sides the equation becomes:
.

.
Next, eliminate the -3 on the left side by adding +3 to both sides. When you do that the
equation becomes:
.

.
Finally you can solve this equation for x by dividing both sides by the multiplier
of x which is 5. Dividing both sides by 5 gives you .
.
Now that you know x is 3, you can return to either of the two equations you originally
were given and replace the x by 3 to solve for y. In order to avoid working with the
fraction, you can return to the second equation:
.

.
Replace the x with +3 to get:
.

.
and the right side terms combine to give you:
.

.
So the common solution to the equations is x = 3 and y = 1 which means the graphs of
these two equations cross at the point (3,1).

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