Use elimination to solve each system of equations.
x+y=3
2x-3y=16
Sketch an area model for each exercise then find the product. 74x92
Multiply the first equation by 3.
3x + 3y = 9
2x - 3y = 16
Add the two equations.
5x = 25
Insert the x value into the first equation and solve for y. Check by inserting both values into the second equation.
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The exercises are not shown and we cannot demonstrate sketches.
74 * 92 = 6,808
To solve the system of equations using elimination, we'll eliminate one variable at a time. Here's how we can do it:
Step 1: Multiply the first equation by 2 to make the coefficient of x in both equations the same.
2(x+y) = 2(3)
2x+2y = 6
Now we have the following system of equations:
2x+2y = 6
2x-3y = 16
Step 2: Subtract the second equation from the first equation to eliminate x.
(2x+2y) - (2x-3y) = 6 - 16
2x+2y - 2x + 3y = -10
5y = -10
Step 3: Solve for y by dividing both sides of the equation by 5.
5y/5 = -10/5
y = -2
Step 4: Substitute the value of y back into one of the original equations to find the value of x. Let's use the first equation:
x + (-2) = 3
x - 2 = 3
Step 5: Solve for x by adding 2 to both sides of the equation.
x - 2 + 2 = 3 + 2
x = 5
Therefore, the solution to the system of equations is x = 5 and y = -2.