13x+11y=70
11x+13y=74
Change that to:
143x + 121y = 770
143x + 169y = 962
Subtract the first equation from the second, thereby eliminating x.
48y = 192
y = 4
Then compute x using either of your equations.
Super
To solve this system of equations, you can use the method of substitution or elimination. We'll use the method of substitution.
Step 1: Solve one equation for one variable in terms of the other variable.
Let's solve the second equation for x:
11x + 13y = 74
11x = 74 - 13y
x = (74 - 13y)/11
Step 2: Substitute the expression for x from step 1 into the other equation.
13x + 11y = 70
13((74 - 13y)/11) + 11y = 70
Step 3: Simplify and solve for y.
(962 - 169y)/11 + 11y = 70
(962 - 169y + 11 * 11y) / 11 = 70
(962 - 169y + 121y) / 11 = 70
(962 - 48y) / 11 = 70
Multiply both sides of the equation by 11 to get rid of the denominator:
962 - 48y = 770
Step 4: Solve for y.
-48y = 770 - 962
-48y = -192
y = (-192) / (-48)
y = 4
Step 5: Substitute the value of y into either of the original equations and solve for x.
Let's use the first equation:
13x + 11y = 70
13x + 11(4) = 70
13x + 44 = 70
13x = 70 - 44
13x = 26
x = 26 / 13
x = 2
The solution to the system of equations is x = 2 and y = 4.
To solve the system of equations:
13x + 11y = 70
11x + 13y = 74
There are several methods we can use, such as substitution, elimination, or matrix methods. Let's use the elimination method.
Multiply the first equation by 11 and the second equation by 13 to create equal coefficients for either x or y in both equations:
(11 * 13x) + (11 * 11y) = 11 * 70
(13 * 11x) + (13 * 13y) = 13 * 74
This simplifies the equations to:
143x + 121y = 770
143x + 169y = 962
Now, subtract the first equation from the second equation:
(143x + 169y) - (143x + 121y) = 962 - 770
This simplifies to:
169y - 121y = 962 - 770
48y = 192
Divide both sides of the equation by 48:
y = 192 / 48
y = 4
Now substitute this value of y back into one of the original equations; let's use the first equation:
13x + 11(4) = 70
13x + 44 = 70
Subtract 44 from both sides:
13x = 70 - 44
13x = 26
Divide both sides by 13:
x = 26 / 13
x = 2
Therefore, the solution to the system of equations is x = 2 and y = 4.