The graph of equations 2x + y = 7 and 5x – 2y = 4
Please answer quickly!
Answers
Answer:
a). 2 - x = 5x - 2x = 3x
y x = 3
x= 10x 4
10x = 3
4 Answer
Answer:
Lets start with the given system of linear equations
2%2Ax%2B1%2Ay=7
5%2Ax-2%2Ay=4
Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to choose y.
Solve for y for the first equation
1%2Ay=7-2%2AxSubtract 2%2Ax from both sides
y=%287-2%2Ax%29 Divide both sides by 1.
Which breaks down and reduces to
y=7-2%2Ax Now we've fully isolated y
Since y equals 7-2%2Ax we can substitute the expression 7-2%2Ax into y of the 2nd equation. This will eliminate y so we can solve for x.
5%2Ax%2B-2%2Ahighlight%28%287-2%2Ax%29%29=4 Replace y with 7-2%2Ax. Since this eliminates y, we can now solve for x.
5%2Ax-2%2A%287%29-2%28-2%29x=4 Distribute -2 to 7-2%2Ax
5%2Ax-14%2B4%2Ax=4 Multiply
5%2Ax-14%2B4%2Ax=4 Reduce any fractions
5%2Ax%2B4%2Ax=4%2B14Add 14 to both sides
5%2Ax%2B4%2Ax=18 Combine the terms on the right side
9%2Ax=18 Now combine the terms on the left side.
cross%28%281%2F9%29%289%2F1%29%29x=%2818%2F1%29%281%2F9%29 Multiply both sides b/y 1%2F9. This will cancel out 9%2F1 and isolate x
So when we multiply 18%2F1 and 1%2F9 (and simplify) we get
x=2 <---------------------------------One answer
Now that we know that x=2, lets substitute that in for x to solve for y
5%282%29-2%2Ay=4 Plug in x=2 into the 2nd equation
10-2%2Ay=4 Multiply
-2%2Ay=4-10Subtract 10 from both sides
-2%2Ay=-6 Combine the terms on the useright side
cross%28%281%2F-2%29%28-2%29%29%2Ay=%28-6%2F1%29%281%2F-2%29 Multiply both sides by 1%2F-2. This will cancel out -2 on the left side.
y=-6%2F-2 Multiply the terms on the right side
y=3 Reduce
So this is the other answer
y=3<---------------------------------Other answer
So our solution is
x=2 and y=3
which can also look like
(2,3)
Notice if we graph the equations (if you need help with graphing, check out this solver)
2%2Ax%2B1%2Ay=7
5%2Ax-2%2Ay=4
we get
graph of 2%2Ax%2B1%2Ay=7 (red) and 5%2Ax-2%2Ay=4 (green) (hint: you may have to solve for y to graph these) intersecting at the blue circle.
and we can see that the two equations intersect at (2,3). This verifies our answer.
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Check:
Plug in (2,3) into the system of equations
Let x=2 and y=3. Now plug those values into the equation 2%2Ax%2B1%2Ay=7
2%2A%282%29%2B1%2A%283%29=7 Plug in x=2 and y=3
4%2B3=7 Multiply
7=7 Add
7=7 Reduce. Since this equation is true the solution works.
So the solution (2,3) satisfies 2%2Ax%2B1%2Ay=7
Let x=2 and y=3. Now plug those values into the equation 5%2Ax-2%2Ay=4
5%2A%282%29-2%2A%283%29=4 Plug in x=2 and y=3
10-6=4 Multiply
4=4 Add
4=4 Reduce. Since this equation is true the solution works.
So the solution (2,3) satisfies 5%2Ax-2%2Ay=4
Since the solution (2,3) satisfies the system of equations
2%2Ax%2B1%2Ay=7
5%2Ax-2%2Ay=4
this verifies our answer.
