math solving and graph?

Question

okay so we have two equations 2x+y=7 and x+y = 3

how would you solve that then graph

directions read Solve by graphing then check algebraically

we have to give a point like ( 0, 0 ) then graph them


EXAMPLE:

x+y=4
2x-y=5

and the answer is 3,1

also how would i graph each problem?

Answer 1

Each is a straight line: y=mx+b.

y=-2x+7 and y=-x+3

Graph the lines, the intersection is at the point (3,-1).

Check by combining the equations.
2x-x+3=7
x=4
y=-1

Answer 2

If you want to just solve it algebraically, first you must change each standard form equation into slope-intercept form.
x+y=4 = y=-x+4
2x-y=5 = y=2x-5
Because y=y, -x+4=2x-5
-x+4=2x-5
3x=9
x=3 Now you have your x value.
Substitute.
x+y=4
3+y=4
y=1 Now you have your y value.
Thus, the solution is (3,1).
You would graph the equations in the slope-intercept form above (y=-x+4 and y=2x-5). The intersection should be (3,1), also known as the solution.
Proof:
3+1=4
4=4
2(3)-1=5
6-1=5
5=5

Answer 3

a million) -10x=5y could be switched over into the slope-intercept sort (y=mx+b) the place m is the slope of the on the instant line (m=upward thrust/run=y/x) and b as a results of fact the y-intercept, this is a piece of intersection of the line and the y-axis. -10x=5y is comparable to y=-10x/5=-2x+0. right here b is 0 and the slope is -2, meaning the line passes in the course of the beginning place and leans on the left at a fee of 2 upward thrust to a minimum of one run. 2) 2x-3y=6 could be solved with the help of the comparable answer as above in any different case you ought to use the intercept-sort. basically divide the consistent 6 with the help of the coefficients of x and y, 2 and -3,respectively, to locate the x and y-intercepts. So the x and y-intercept are 3 and -2. respectively. To graph the line, plot the intercepts (3,0) and (0,-2) on the Cartesian airplane then connect those factors, the line could be prolonged infinitely.