review the graphs of a system of two linear equations in two varibles: x-5y=7 and 3x-2y=-4. find the solution to both equations The intersection point is
where the two lines representing the system of equations intersect. To find this intersection point, we can solve the system of equations simultaneously.
Given equations:
1) x - 5y = 7
2) 3x - 2y = -4
To solve the system of equations, we can use the method of substitution or elimination. Let's use the elimination method.
Step 1: Multiply the first equation by 3 and the second equation by 1 to make the coefficients of x in both equations the same.
3(x - 5y) = 3(7) becomes 3x - 15y = 21
3(3x - 2y) = 3(-4) becomes 9x - 6y = -12
Step 2: Subtract the second equation from the first equation to eliminate x.
(3x - 15y) - (9x - 6y) = 21 - (-12)
-6x - 9y = 33
Step 3: Solve for y.
-6x - 9y = 33
-9y = 6x + 33
y = (6x + 33)/-9
y = -2/3x - 11/3
Step 4: Substitute the value of y back into one of the original equations to solve for x.
x - 5(-2/3x - 11/3) = 7
x + 10/3x + 55/3 = 7
(3x + 10x + 55)/3 = 7
13x + 55 = 21
13x = -34
x = -34/13
Step 5: Substitute the value of x back into the equation found in step 3 to solve for y.
y = -2/3(-34/13) - 11/3
y = 68/39 - 143/39
y = -75/39
y = -25/13
Therefore, the solution to both equations is x = -34/13 and y = -25/13. The intersection point where the two lines intersect is (-34/13, -25/13).