X2+y2=34,x+y=2 solve for simultaneous quadratic equation
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To solve the simultaneous quadratic equations x^2 + y^2 = 34 and x + y = 2, we can use the method of substitution or elimination.
Let's start with the method of substitution:
Step 1: Solve one equation for one variable in terms of the other variable.
From the second equation, we can isolate x or y. Let's solve for x:
x + y = 2
x = 2 - y
Step 2: Substitute the expression from step 1 into the other equation.
Substitute the x expression (2 - y) into the first equation:
(2 - y)^2 + y^2 = 34
Step 3: Simplify and solve the resulting quadratic equation.
Expand the squared term:
4 - 4y + y^2 + y^2 = 34
2y^2 - 4y + 4 = 34
Rearrange the equation:
2y^2 - 4y - 30 = 0
Divide all terms by 2 to simplify:
y^2 - 2y - 15 = 0
Now we have a quadratic equation in terms of y. Solve this equation by factoring or using the quadratic formula.
Factoring: (y - 5)(y + 3) = 0
Therefore, y - 5 = 0 or y + 3 = 0
y = 5 or y = -3
Step 4: Substitute the values found in step 3 into the expression from step 1 to find the corresponding x-values.
For y = 5:
x = 2 - y
x = 2 - 5
x = -3
For y = -3:
x = 2 - y
x = 2 - (-3)
x = 5
Therefore, the solutions to the simultaneous quadratic equations are x = -3, y = 5 and x = 5, y = -3.
x^2 + y^2 = 34
x+y = 2
Since y = 2-x, find x using
x^2 + (2-x)^2 = 34
Once you have x, then get y=2-x