What is the solution to the system
7x+5y=19
-7x-2y=-16
a.(2,1)
b.(1,2)
c.(7,5)
d.(-7,-2)
Is it a. or b.?
Substitute the numbers for the letters in the equations. Which is correct -- a or b?
Was b. correct Ms. Sue?
And can you help me with one more?
what is the solution of the system
y=-3x
3x+2y=6
a. 2, 6
b. -1, 3
c. -2, 6
d. 1.5, -4.5
Substitute.
7x+5y=19
7 + 10 does not equal 19.
To solve the given system of equations, we can use the method of elimination or substitution.
Let's use the method of elimination:
Step 1: Multiply the second equation by -1 to get rid of the -7x term:
-1(-7x - 2y) = -1(-16)
7x + 2y = 16
Step 2: Now, add the two equations together to eliminate the x-term:
(7x + 5y) + (7x + 2y) = 19 + 16
14x + 7y = 35
Step 3: Divide the entire equation by 7 to simplify it:
(14x + 7y)/7 = 35/7
2x + y = 5
Now, we have a new equation 2x + y = 5.
Step 4: Solve the new equation simultaneously with either the first or second equation. Let's use the first equation:
7x + 5y = 19
Multiply the equation by -2 to make the coefficients of y match in both equations:
-2(2x + y) = -2(5)
-4x - 2y = -10
Step 5: Add the two equations together to eliminate the y-term:
(7x + 5y) + (-4x - 2y) = 19 - 10
3x + 3y = 9
Step 6: Divide the entire equation by 3 to simplify it:
(3x + 3y)/3 = 9/3
x + y = 3
Now, we have a new equation x + y = 3.
Step 7: Solve the new equation simultaneously with the first equation:
7x + 5y = 19
Rearrange the second equation to solve for y:
y = 3 - x
Substitute this value of y in the first equation:
7x + 5(3 - x) = 19
7x + 15 - 5x = 19
2x + 15 = 19
2x = 4
x = 2
Step 8: Substitute the value of x in any of the three equations to solve for y:
Using the first equation:
7(2) + 5y = 19
14 + 5y = 19
5y = 19 - 14
5y = 5
y = 1
Therefore, the solution to the system of equations is (x, y) = (2, 1).
So, the correct answer is option a. (2, 1).