I'm confused about graphing or solving the linear equations for slope/intercept.
Here is what I solved:
3x+2y=-6 X-4y=-16
2y= -3x-6 -4y=1x-16
Y=-3/2+3 Y=+1/4+4
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My answer for graphing the systems for the lines to intersect...well, they didn't intersect. But the answer is (4,-1)
Can someone explain my problem? And help explain how to solve it?
I'm confused by your impatience and reposting the same problem...
To solve a system of linear equations, such as the one you provided, you have two main methods: graphing and substitution/elimination. Graphing involves plotting the equations on a coordinate plane to find their point of intersection, while substitution/elimination involves manipulating the equations to solve for one variable and then substituting that value into the other equation. Let's go through both methods for your equations:
Method 1: Graphing
To graph the equations, you need to get them in slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.
For the first equation, 3x + 2y = -6, rearrange it:
2y = -3x - 6
Divide everything by 2:
y = (-3/2)x - 3
For the second equation, x - 4y = -16, rearrange it:
-4y = -x - 16
Divide everything by -4 and remember to reverse the sign:
y = (1/4)x + 4
Now that you have both equations in slope-intercept form, you can graph them on a coordinate plane. The first equation has a slope of -3/2 and a y-intercept of -3. The second equation has a slope of 1/4 and a y-intercept of 4. Plotting the lines, you will see that they do not intersect. Hence, there is no solution to this system of equations.
However, if you were given the answer (4, -1) and you want to check if it satisfies the equations, substitute these values into both equations and see if they hold true. In this case, substituting x = 4 and y = -1 into both equations, you will find that they do not satisfy either equation. Therefore, (4, -1) is not a solution to this system of equations.
Method 2: Substitution/Elimination
Let's solve the system using the substitution method:
Start with the first equation: 3x + 2y = -6
Solve for x:
x = (-2y - 6)/3
Substitute this expression for x into the second equation:
x - 4y = -16
((-2y - 6)/3) - 4y = -16
Now, you can solve for y:
(-2y - 6)/3 - 4y = -16
Multiply everything by 3 to eliminate the denominator:
-2y - 6 - 12y = -48
Combine like terms:
-14y - 6 = -48
Add 6 to both sides:
-14y = -42
Divide everything by -14:
y = 3
Next, substitute this value back into the first equation to solve for x:
3x + 2(3) = -6
3x + 6 = -6
3x = -12
x = -4
So the solution to the system of equations is (x, y) = (-4, 3), not (4, -1). Therefore, please double-check your work or problem statement to confirm the correct solution.