Solve the system of equations. 3x + y = 2 and 7x- 4y = 30, which of the following answers is correct? (2, -2), (1/2, 1/2), (2, -4) or (-2, 8)?
To solve this system of equations, we can use the method of substitution or elimination.
Let's use the method of substitution.
From the first equation, we can solve for y in terms of x:
3x + y = 2
y = 2 - 3x
Now, substitute this expression for y in the second equation:
7x - 4(2 - 3x) = 30
7x - 8 + 12x = 30
19x - 8 = 30
19x = 38
x = 38/19
x = 2
Now, substitute this value of x back into the first equation to solve for y:
3(2) + y = 2
6 + y = 2
y = 2 - 6
y = -4
Therefore, the correct answer is (2, -4).
Are you sure double check please?
Apologies for the incorrect response. Let's double-check the calculations.
From the first equation, we can solve for y in terms of x:
3x + y = 2
y = 2 - 3x
Now, substitute this expression for y in the second equation:
7x - 4(2 - 3x) = 30
7x - 8 + 12x = 30
19x - 8 = 30
19x = 38
x = 38/19
x = 2
Now, substitute this value of x back into the first equation to solve for y:
3(2) + y = 2
6 + y = 2
y = 2 - 6
y = -4
Therefore, the correct answer is (2, -4).
How many solutions does the system of equations have -5x + 7 = -18 and 10x- 2y = 36 , two two, infinite, none or one?
To determine the number of solutions in the system of equations, we can analyze the equations individually.
The first equation, -5x + 7 = -18, is a linear equation in one variable. By solving this equation, we can find the value of x.
-5x + 7 = -18
Subtract 7 from both sides: -5x = -25
Divide by -5: x = 5
The second equation, 10x - 2y = 36, is a linear equation in two variables. The coefficients of x and y are both non-zero and the equation is not a multiple of the other equation.
To determine the number of solutions, we can rearrange the equation in slope-intercept form y = mx + b, where m represents the slope.
10x - 2y = 36
Rearrange: -2y = -10x + 36
Divide by -2: y = 5x - 18
Since the slope, 5, is not equal to the slope in the first equation (which is 0 since it only contains x), the lines represented by the two equations are not parallel.
Therefore, the system of equations has one solution.
Are you sure? Double check please
Apologies for the incorrect response. Let's double-check the calculations.
The first equation is -5x + 7 = -18.
Add 5x to both sides:
7 = 5x - 18
Add 18 to both sides:
25 = 5x
Divide both sides by 5:
x = 5
Now let's check the second equation: 10x - 2y = 36.
Substitute the value of x we found:
10(5) - 2y = 36
Simplify:
50 - 2y = 36
Subtract 50 from both sides:
-2y = -14
Divide both sides by -2:
y = 7
Therefore, the system of equations has one solution, which is (5, 7).