Could you please check my answers we are using substitution to solve each system of equations. And at the end of every solution you are supposed to have an answer as a coordinate.

1. x=2y
x+y=3
Answer (1,2)

2. 2y=3
x-y=10
Answer: (10,10)

3. y=x+7
x+2y= -21
Answer: (-3,-4)

4. 2y=x
x-y=10
Answer: (6,1)

5. x+y=0
4x+4y=0
Answer: (0,0)

6. 2x-y=6
3x-5y=9
Answer: (3,0)

7. 4x-y= -6
y+2=x
Answer: (-8,30)

8. 4x-y= -3
Answer: (3,-6)

9. x-5y=11
3x+y=7
Answer: infinitely many

10. x-2y=5
3x-5y=8
Answer: (-1.75, -8.5)

11. Laura and Ji- Yong were jogging on a 10 mile path. Laura had a 2-mile head start on Ju- Yong. If Laura ran at an average rate of 5 miles per hour and Ji-Yong ran at an average rate of 8 miles per hour, how long would it take for Ji-Yong to catch up with Laura.
Answer: 4 miles.

none of your equation answers are correct.

I will #3 for you then follow the same method to do the rest

3. y=x+7
x+2y= -21

sub the first into the second:
x + 2(x+7) = -21
x + 2x + 14 = -21
3x = -35
x = -35/3
now sub that back into the first
y = -35/3 + 7 = -35/3 + 21/3 = -14/3

check:
in #1
LS = y = -14/3
RS = x+7 = -35/3 + 7 = -14/3

in #2
LS = x+2y = -35/3 + 2(-14/3) = -21
RS = -21

now work each one out the same way, and check your answer the same way.

If you know how to do this substitution let me know but if you don't that's okay. Also, the last one I redid I got 52:30

x-2y=-1 -x+5y=4 x=-1 y=1

1. To solve the first system of equations using substitution, we start by solving one of the equations for one variable and substitute it into the other equation.

Given:
x = 2y
x + y = 3

Substitute x = 2y into the second equation:
2y + y = 3
3y = 3
y = 1

Now substitute y = 1 into the first equation:
x = 2(1)
x = 2

Therefore, the solution to the system of equations is (x, y) = (2, 1).

2. Given:
2y = 3
x - y = 10

Solve the first equation for y:
y = 3/2

Substitute y = 3/2 into the second equation:
x - (3/2) = 10
x = 10 + (3/2)
x = 20/2 + 3/2
x = 23/2

Therefore, the solution to the system of equations is (x, y) = (23/2, 3/2) or approximately (11.5, 1.5).

3. Given:
y = x + 7
x + 2y = -21

Substitute y = x + 7 into the second equation:
x + 2(x + 7) = -21
x + 2x + 14 = -21
3x = -35
x = -35/3

Substitute x = -35/3 into the first equation:
y = (-35/3) + 7
y = -35/3 + 21/3
y = -14/3

Therefore, the solution to the system of equations is (x, y) = (-35/3, -14/3) or approximately (-11.67, -4.67).

4. Given:
2y = x
x - y = 10

Substitute 2y = x into the second equation:
2y - y = 10
y = 10

Now substitute y = 10 into the first equation:
2(10) = x
x = 20

Therefore, the solution to the system of equations is (x, y) = (20, 10).

5. Given:
x + y = 0
4x + 4y = 0

The first equation tells us that x = -y. Substitute this into the second equation:
4(-y) + 4y = 0
-4y + 4y = 0
0 = 0

Since 0 = 0, the two equations represent the same line, and any value for x and y that satisfies the first equation will also satisfy the second equation. In this case, (x, y) = (0, 0) is a solution.

Therefore, there are infinitely many solutions to the system of equations.

6. Given:
2x - y = 6
3x - 5y = 9

Solve the first equation for y:
y = 2x - 6

Substitute y = 2x - 6 into the second equation:
3x - 5(2x - 6) = 9
3x - 10x + 30 = 9
-7x = -21
x = 3

Substitute x = 3 into the first equation:
2(3) - y = 6
6 - y = 6
- y = 0
y = 0

Therefore, the solution to the system of equations is (x, y) = (3, 0).

7. Given:
4x - y = -6
y + 2 = x

Solve the second equation for x:
x = y + 2

Substitute x = y + 2 into the first equation:
4(y + 2) - y = -6
4y + 8 - y = -6
3y = -14
y = -14/3

Substitute y = -14/3 into the second equation:
x = (-14/3) + 2
x = (-14/3) + (6/3)
x = -8/3

Therefore, the solution to the system of equations is (x, y) = (-8/3, -14/3) or approximately (-2.67, -4.67).

8. Given:
4x - y = -3

Since there is only one equation, we can solve for either variable. Let's solve for y:
y = 4x + 3

There is no specific coordinate since we are only given a single equation.

9. Given:
x - 5y = 11
3x + y = 7

To solve this system, we can use the method of substitution. Solve the second equation for y:
y = 7 - 3x

Substitute y = 7 - 3x into the first equation:
x - 5(7 - 3x) = 11
x - 35 + 15x = 11
16x - 35 = 11
16x = 46
x = 46/16

Substitute x = 46/16 into the second equation:
3(46/16) + y = 7
69/16 + y = 7
y = 112/16 - 69/16
y = 43/16

Therefore, the solution to the system of equations is (x, y) = (46/16, 43/16) or approximately (2.88, 2.69).

10. Given:
x - 2y = 5
3x - 5y = 8

To solve this system, we can use the method of substitution. Solve the first equation for x:
x = 5 + 2y

Substitute x = 5 + 2y into the second equation:
3(5 + 2y) - 5y = 8
15 + 6y - 5y = 8
y = -7

Now substitute y = -7 into the first equation:
x - 2(-7) = 5
x + 14 = 5
x = -9

Therefore, the solution to the system of equations is (x, y) = (-9, -7).

11. In this question, we need to find the time it takes for Ji-Yong to catch up with Laura. We can solve this by setting up an equation based on their respective rates and distances traveled.

Let the time taken by Ji-Yong be represented by t.

Laura had a 2-mile head start, so Ji-Yong had to catch up on this distance to be at the same point.

The distance Laura traveled is 10 miles. Ji-Yong traveled at a rate of 8 miles per hour, so the distance he covered in time t is 8t.

Now we can set up the equation:

Distance covered by Laura = Distance covered by Ji-Yong
10 = 8t + 2

Solve for t:
8t = 10 - 2
8t = 8
t = 1

Therefore, it would take Ji-Yong 1 hour to catch up with Laura, and they would be at the same point 4 miles from the starting point.